Module 5

Options Theory for Professional Trading

Module 5 — Options Theory for Professional Trading

Chapter 1

Call Option Basics

246

1.1– Breaking the Ice

As with any of the previous modules in Varsity, we will again make the same old

assumption that you are new to options and therefore know nothing about options.

For this reason we will start from scratch and slowly ramp up as we proceed. Let us

start with running through some basic background information.

The options market makes up for a significant part of the derivative market,

particularly in India. I would not be exaggerating if I were to say that nearly 80% of

the derivatives traded are options and the rest is attributable to the futures market.

Internationally, the option market has been around for a while now, here is a quick

background on the same –

o Custom options were available as Over the Counter (OTC) since the 1920’s. These

options were mainly on commodities

o Options on equities began trading on the Chicago Board Options Exchange (CBOE)

in 1972

o Options on currencies and bonds began in late 1970s. These were again OTC trades

o Exchange-traded options on currencies began on Philadelphia Stock Exchange in

1982

o Interest rate options began trading on the CME in 1985

Clearly the international markets have evolved a great deal since the OTC days.

However in India from the time of inception, the options market was facilitated by

the exchanges. However options were available in the off market ‘Badla’ system.

Think of the ‘badla system’ as a grey market for derivatives transactions. The badla

system no longer exists, it has become obsolete. Here is a quick recap of the history

of the Indian derivative markets –

o June 12th 2000 – Index futures were launched

o June 4th 2001 –Index options were launched

o July 2nd 2001 – Stock options were launched

o November 9th 2001 – Single stock futures were launched.

Though the options market has been around since 2001, the real liquidity in the

Indian index options was seen only in 2006! I remember trading options around that

time, the spreads were high and getting fills was a big deal. However in 2006, the

Ambani brothers formally split up and their respective companies were listed as

separate entities, thereby unlocking the value to the shareholders. In my opinion

this particular corporate event triggered vibrancy in the Indian markets, creating

some serious liquidity. However if you were to compare the liquidity in Indian stock

options with the international markets, we still have a long way to catch up.

1.2 – A Special Agreement

There are two types of options – The Call option and the Put option. You can be a

buyer or seller of these options. Based on what you choose to do, the P&L profile

changes. Of course we will get into the P&L profile at a much later stage. For now,

let us understand what “The Call Option” means. In fact the best way to understand

the call option is to first deal with a tangible real world example, once we

understand this example we will extrapolate the same to stock markets. So let’s get

started.

Consider this situation; there are two good friends, Ajay and Venu. Ajay is actively

evaluating an opportunity to buy 1 acre of land that Venu owns. The land is valued

at Rs.500,000/-. Ajay has been informed that in the next 6 months, a new highway

project is likely to be sanctioned near the land that Venu owns. If the highway

indeed comes up, the valuation of the land is bound to increase and therefore Ajay

would benefit from the investment he would make today. However if the ‘highway

news’ turns out to be a rumor- which means Ajay buys the land from Venu today

and there is no highway tomorrow, then Ajay would be stuck with a useless piece of

land!

So what should Ajay do? Clearly this situation has put Ajay in a dilemma as he is

uncertain whether to buy the land from Venu or not. While Ajay is muddled in this

thought, Venu is quite clear about selling the land if Ajay is willing to buy.

Ajay wants to play it safe, he thinks through the whole situation and finally proposes

a special structured arrangement to Venu, which Ajay believes is a win-win for both

of them, the details of the arrangement is as follows –

1. Ajay pays an upfront fee of Rs.100,000/- today. Consider this as a non refundable

agreement fees that Ajay pays

2. Against this fees, Venu agrees to sell the land after 6 months to Ajay

3. The price of the sale( which is expected 6 months later) is fixed today at Rs.500,000/-

4. Because Ajay has paid an upfront fee, only he can call off the deal at the end of 6

months (if he wants to that is), Venu cannot

5. In the event Ajay calls off the deal at the end of 6 months, Venu gets to keep the

upfront fees

So what do you think about this special agreement? Who do you think is smarter

here – Is it Ajay for proposing such a tricky agreement or Venu for accepting such an

agreement? Well, the answer to these questions is not easy to answer, unless you

analyze the details of the agreement thoroughly. I would suggest you read through

the example carefully (it also forms the basis to understand options) – Ajay has

plotted an extremely clever deal here! In fact this deal has many faces to it.

Let us break down Ajay’s proposal to understand some details –

o By paying an agreement fee of Rs.100,000/-, Ajay is binding Venu into an obligation.

He is forcing Venu to lock the land for him for the next 6 months

o Ajay is fixing the sale price of the land based on today’s price i.e Rs.500,000/- which

means irrespective of what the price would be 6 months later he gets to buy the

land at today’s price. Do note, he is fixing a price and paying an additional

Rs.100,000/- today

o At the end of the 6 months, if Ajay does not want to buy the land he has the right to

say ‘no’ to Venu, but since Venu has taken the agreement fee from Ajay, Venu will

not be in a position to say no to Ajay

o The agreement fee is non negotiable, non refundable

Now, after initiating this agreement both Ajay and Venu have to wait for the next 6

months to figure out what would actually happen. Clearly, the price of the land will

vary based on the outcome of the ‘highway project’. However irrespective of what

happens to the highway, there are only three possible outcomes –

1. Once the highway project comes up, the price of the land would go up, say it shoots

up to Rs.10,00,000/-

2. The highway project does not come up, people are disappointed, the land price

collapses, say to Rs.300,000/-

3. Nothing happens, price stays flat at Rs.500,000/-

I’m certain there could be no other possible outcomes that can occur apart from the

three mentioned above.

We will now step into Ajay’s shoes and think through what he would do in each of

the above situations.

Scenario 1 – Price goes up to Rs.10,00,000/-

Since the highway project has come up as per Ajay’s expectation, the land price has

also increased. Remember as per the agreement, Ajay has the right to call off the

deal at the end of 6 months. Now, with the increase in the land price, do you think

Ajay will call off the deal? Not really, because the dynamics of the sale are in Ajay’s

favor –

Current Market price of the land = Rs.10,00,000/-

Sale agreement value = Rs.500,000/-

This means Ajay now enjoys the right to buy a piece of land at Rs.500,000/- when in

the open market the same land is selling at a much higher value of – Rs.10,00,000/-.

Clearly Ajay is making a steal deal here. Hence he would go ahead and demand

Venu to sell him the land. Venu is obligated to sell him the land at a lesser value,

simply because he had accepted Rs.100,000/- agreement fees from Ajay 6 months

earlier.

So how much money is Ajay making? Well, here is the math –

Buy Price = Rs.500,000/-

Add: Agreement Fees = Rs.100,000/- (remember this is a non refundable amount)

Total Expense = 500,000 + 100,000 = 600,000/-

Current Market of the land = Rs.10,00,000/-

Hence his profit is Rs.10,00,000 – Rs.600,000 = Rs.400,000/-

Another way to look at this is – For an initial cash commitment of Rs.100,000/- Ajay

is now making 4 times the money! Venu even though very clearly knows that the

value of the land is much higher in the open market, is forced to sell it at a much

lower price to Ajay. The profit that Ajay makes (Rs.400,000/-) is exactly the notional

loss that Venu would incur.

Scenario 2 – Price goes down to Rs.300,000/-

It turns out that the highway project was just a rumor, and nothing really is

expected to come out of the whole thing. People are disappointed and hence there

is a sudden rush to sell out the land. As a result, the price of the land goes down to

Rs.300,000/-.

So what do you think Ajay will do now? Clearly it does not make sense to buy the

land, hence he would walk away from the deal. Here is the math that explains why it

does not make sense to buy the land –

Remember the sale price is fixed at Rs.500,000/-, 6 months ago. Hence if Ajay has to

buy the land he has to shell out Rs.500,000/- plus he had paid Rs.100,000/- towards

the agreement fees. Which means he is in effect paying Rs.600,000/- to buy a piece

of land worth just Rs.300,000/-. Clearly this would not make sense to Ajay, since he

has the right to call of the deal, he would simply walk away from it and would not

buy the land. However do note, as per the agreement Ajay has to let go of

Rs.100,000/-, which Venu gets to pocket.

Scenario 3 – Price stays at Rs.500,000/-

For whatever reasons after 6 months the price stays at Rs.500,000/- and does not

really change. What do you think Ajay will do? Well, he will obviously walk away from

the deal and would not buy the land. Why you may ask, well here is the math –

Cost of Land = Rs.500,000/-

Agreement Fee = Rs.100,000/-

Total = Rs.600,000/-

Value of the land in open market = Rs.500,000/-

Clearly it does not make sense to buy a piece of land at Rs.600,000/- when it is

worth Rs.500,000/-. Do note, since Ajay has already committed 1lk, he could still buy

the land, but ends up paying Rs 1lk extra in this process. For this reason Ajay will call

off the deal and in the process let go of the agreement fee of Rs.100,000/- (which

Venu obviously pockets).

I hope you have understood this transaction clearly, and if you have then it is good

news as through the example you already know how the call options work! But let

us not hurry to extrapolate this to the stock markets; we will spend some more time

with the Ajay-Venu transaction.

Here are a few Q&A’s about the transaction which will throw some more light on the

example –

1. Why do you think Ajay took such a bet even though he knows he will lose his 1 lakh

if land prices does not increase or stays flat?

1. Agreed Ajay would lose 1 lakh, but the best part is that Ajay knows his maximum loss (which is 1

lakh) before hand. Hence there are no negative surprises for him. Also, as and when the land

prices increases, so would his profits (and therefore his returns). At Rs.10,00,000/- he would be

making Rs.400,000/- profit on his investment of Rs.100,000/- which is 400%.

2. Under what circumstances would a position such as Ajay’s make sense?

1. Only that scenario when the price of the land increases

3. Under what circumstances would Venu’s position makes sense

1. Only that scenario when the price of the land decreases of stays flat

4. Why do you think Venu is taking such a big risk? He would lose a lot of money if the

land prices increases after 6 months right?

1. Well, think about it. There are only 3 possible scenarios, out which 2 indeed benefit Venu.

Statistically, Venu has 66.66% chances of winning the bet as opposed to Ajay’s 33.33% chance

Let us summarize a few important points now –

o The payment from Ajay to Venu ensures that Ajay has a right (remember only he

can call off the deal) and Venu has an obligation (if the situation demands, he has to

honor Ajay’s claim)

o The outcome of the agreement at termination (end of 6 months) is determined by

the price of the land. Without the land, the agreement has no value

o Land is therefore called an underlying and the agreement is called a derivative

o An agreement of this sort is called an “Options Agreement”

o Since Venu has received the advance from Ajay, Venu is called the ‘agreement seller

or Writer’ and Ajay is called the ‘agreement buyer’

o In other words since this agreement is called “an options agreement”, Ajay can be

called an Options Buyer and Venu the Options Seller/writer.

o The agreement is entered after the exchange of 1 lakh, hence 1 lakh is the price of

this option agreement. This is also called the “Premium” amount

o Every variable in the agreement – Area of the land, price and the date of sale is

fixed.

o As a thumb rule, in an options agreement the buyer always has a right and the seller

has an obligation

I would suggest you be absolutely thorough with this example. If not, please go

through it again to understand the dynamics involved. Also, please remember this

example, as we will revisit the same on a few occasions in the subsequent chapters.

Let us now proceed to understand the same example from the stock market

perspective.

1.3 – The Call Option

Let us now attempt to extrapolate the same example in the stock market context

with an intention to understand the ‘Call Option’. Do note, I will deliberately skip the

nitty-gritty of an option trade at this stage. The idea is to understand the bare bone

structure of the call option contract.

Assume a stock is trading at Rs.67/- today. You are given a right today to buy the

same one month later, at say Rs. 75/-, but only if the share price on that day is more

than Rs. 75, would you buy it?. Obviously you would, as this means to say that after

1 month even if the share is trading at 85, you can still get to buy it at Rs.75!

In order to get this right you are required to pay a small amount today, say Rs.5.0/-.

If the share price moves above Rs. 75, you can exercise your right and buy the

shares at Rs. 75/-. If the share price stays at or below Rs. 75/- you do not exercise

your right and you do not need to buy the shares. All you lose is Rs. 5/- in this case.

An arrangement of this sort is called Option Contract, a ‘Call Option’ to be precise.

After you get into this agreement, there are only three possibilities that can occur.

And they are-

1. The stock price can go up, say Rs.85/-

2. The stock price can go down, say Rs.65/-

3. The stock price can stay at Rs.75/-

Case 1 – If the stock price goes up, then it would make sense in exercising your right

and buy the stock at Rs.75/-.

The P&L would look like this –

Price at which stock is bought = Rs.75

Premium paid =Rs. 5

Expense incurred = Rs.80

Current Market Price = Rs.85

Profit = 85 – 80 = Rs.5/-

Case 2 – If the stock price goes down to say Rs.65/- obviously it does not makes

sense to buy it at Rs.75/- as effectively you would spending Rs.80/- (75+5) for a stock

that’s available at Rs.65/- in the open market.

Case 3 – Likewise if the stock stays flat at Rs.75/- it simply means you are spending

Rs.80/- to buy a stock which is available at Rs.75/-, hence you would not invoke your

right to buy the stock at Rs.75/-.

This is simple right? If you have understood this, you have essentially understood

the core logic of a call option. What remains unexplained is the finer points, all of

which we will learn soon.

At this stage what you really need to understand is this – For reasons we have

discussed so far whenever you expect the price of a stock (or any asset for that

matter) to increase, it always makes sense to buy a call option!

Now that we are through with the various concepts, let us understand options and

their associated terms

Variable

Ajay – Venu

Transaction

Stock

Example

Remark

Underlying

1 acre land

Stock

Do note the concept of lot size is applicable in options. So

just like in the land deal where the deal was on 1 acre

land, not more or not less, the option contract will be the

lot size

Expiry

6 months

1 month

Like in futures there are 3 expiries available

Reference

Price

Rs.500,000/-

Rs.75/-

This is also called the strike price

Premium

Rs.100,000/-

Rs.5/-

Do note in the stock markets, the premium changes on a

minute by minute basis. We will understand the logic soon

Regulator

None, based on

good faith

Stock

Exchange

All options are cash settled, no defaults have occurred

until now.

Finally before I end this chapter, here is a formal definition of a call options contract

–

“The buyer of the call option has the right, but not the obligation to buy an agreed

quantity of a particular commodity or financial instrument (the underlying) from the

seller of the option at a certain time (the expiration date) for a certain price (the strike

price). The seller (or “writer”) is obligated to sell the commodity or financial instrument

should the buyer so decide. The buyer pays a fee (called a premium) for this right”.

In the next chapter we will look into a few finer details with regard to the ‘Call

Option’.

Key takeaways form this chapter

1. Options are traded in the Indian markets for over 15 years, but the real liquidity was

available only since 2006

2. An Option is a tool for protecting your position and reducing risk

3. A buyer of the call option has the right and the seller has an obligation to make

delivery

4. The option is only given to one party in the transaction ( buyer of an option)

5. The option seller is also called the option writer

6. At the time of agreement the option buyer pays a certain amount to the option

seller, this is called the ‘Premium’ amount

7. The agreement happens at a pre specified price, often called the ‘Strike Price’

8. The option buyer benefits only if the price of the asset increases higher than the

strike price

9. If the asset price stays at or below the strike, the buyer does not benefit, for this

reason it always makes sense to buy options when you expect the price to increase

10. Statistically the option seller has higher odds of winning in an typical option contract

11. The directional view has to pan out before the expiry date, else the option will

expire worthless

Module 5 — Options Theory for Professional Trading

Chapter 2

Basic Option Jargons

165

2.1– Decoding the basic jargons

In the previous chapter, we understood the basic call option structure. The idea of

the previous chapter was to capture a few essential ‘Call Option’ concepts such as –

1. It makes sense to be a buyer of a call option when you expect the underlying price

to increase

2. If the underlying price remains flat or goes down then the buyer of the call option

loses money

3. The money the buyer of the call option would lose is equivalent to the premium

(agreement fees) the buyer pays to the seller/writer of the call option.

In the next chapter i.e. Call Option (Part 2), we will attempt to understand the call

option in a bit more detail. However before we proceed further let us decode a few

basic option jargons. Discussing these jargons at this stage will not only strengthen

our learning, but will also make the forthcoming discussion on the options easier to

comprehend.

Here are a few jargons that we will look into –

1. Strike Price

2. Underlying Price

3. Exercising of an option contract

4. Option Expiry

5. Option Premium

6. Option Settlement

Do remember, since we have only looked at the basic structure of a call option, I

would encourage you to understand these jargons only with respect to the call

option.

Strike Price

Consider the strike price as the anchor price at which the two parties (buyer and

seller) agree to enter into an options agreement. For instance, in the previous

chapter’s ‘Ajay – Venu’ example the anchor price was Rs.500,000/-, which is also the

‘Strike Price’ for their deal. We also looked into a stock example where the anchor

price was Rs.75/-, which is also the strike price. For all ‘Call’ options the strike price

represents the price at which the stock can be bought on the expiry day.

For example, if the buyer is willing to buy ITC Limited’s Call Option of Rs.350 (350

being the strike price) then it indicates that the buyer is willing to pay a premium

today to buy the rights of ‘buying ITC at Rs.350 on expiry’. Needless to say he will

buy ITC at Rs.350, only if ITC is trading above Rs.350.

In fact here is a snap shot from NSE’s website where I have captured different strike

prices of ITC and the associated premium.

The table that you see above is called an ‘Option Chain’, which basically lists all the

different strike prices available for a contract along with the premium for the same.

Besides this information, the option chain has a lot more trading information such

as Open Interest, volume, bid-ask quantity etc. I would suggest you ignore all of it

for now and concentrate only on the highlighted information –

1. The highlight in maroon shows the price of the underlying in the spot. As we can see

at the time of this snapshot ITC was trading at Rs.336.9 per share

2. The highlight in blue shows all the different strike prices that are available. As we

can see starting from Rs.260 (with Rs.10 intervals) we have strike prices all the way

up to Rs.480

3. Do remember, each strike price is independent of the other. One can enter into an

options agreement , at a specific strike price by paying the required premium

4. For example one can enter into a 340 call option by paying a premium of Rs.4.75/-

(highlighted in red)

1. This entitles the buyer to buy ITC shares at the end of expiry at Rs.340. Of course, you now know

under which circumstance it would make sense to buy ITC at 340 at the end of expiry

Underlying Price

As we know, a derivative contract derives its value from an underlying asset. The

underlying price is the price at which the underlying asset trades in the spot market.

For example in the ITC example that we just discussed, ITC was trading at

Rs.336.90/- in the spot market. This is the underlying price. For a call option, the

underlying price has to increase for the buyer of the call option to benefit.

Exercising of an option contract

Exercising of an option contract is the act of claiming your right to buy the options

contract at the end of the expiry. If you ever hear the line “exercise the option

contract” in the context of a call option, it simply means that one is claiming the

right to buy the stock at the agreed strike price. Clearly he or she would do it only if

the stock is trading above the strike. Here is an important point to note – you can

exercise the option only on the day of the expiry and not anytime before the expiry.

Hence, assume with 15 days to expiry one buys ITC 340 Call option when ITC is

trading at 330 in the spot market. Further assume, after he buys the 340 call option,

the stock price increases to 360 the very next day. Under such a scenario, the option

buyer cannot ask for a settlement (he cannot exercise) against the call option he

holds. Settlement will happen only on the day of the expiry, based on the price the

asset is trading in the spot market on the expiry day.

Option Expiry

Similar to a futures contract, options contract also has expiry. In fact both equity

futures and option contracts expire on the last Thursday of every month. Just like

futures contracts, option contracts also have the concept of current month, mid

month, and far month. Have a look at the snapshot below –

This is the snapshot of the call option to buy Ashok Leyland Ltd at the strike price of

Rs.70 at Rs.3.10/-. As you can see there are 3 expiry options – 26

March 2015

(current month), 30

April 2015 (mid month), and 28

May 2015 (far month). Of

course the premium of the options changes as and when the expiry changes. We

will talk more about it at an appropriate time. But at this stage, I would want you to

remember just two things with respect to expiry – like futures there are 3 expiry

options and the premium is not the same across different expiries.

Option Premium

Since we have discussed premium on a couple instances previously, I guess you

would now be clear about a few things with respect to the ‘Option Premium’.

Premium is the money required to be paid by the option buyer to the option

seller/writer. Against the payment of premium, the option buyer buys the right to

exercise his desire to buy (or sell in case of put options) the asset at the strike price

upon expiry.

If you have got this part clear till now, I guess we are on the right track. We will now

proceed to understand a new perspective on ‘Premiums’. Also, at this stage I guess it

is important to let you know that the whole of option theory hinges upon ‘Option

Premium’. Option premiums play an extremely crucial role when it comes to trading

options. Eventually as we progress through this module you will see that the

discussions will be centered heavily on the option premium.

Let us revisit the ‘Ajay-Venu’ example, that we took up in the previous chapter.

Consider the circumstances under which Venu accepted the premium of

Rs.100,000/- from Ajay –

1. News flow – The news on the highway project was only speculative and no one

knew for sure if the project would indeed come up

1. Think about it, we discussed 3 possible scenarios in the previous chapter out of which 2 were

favorable to Venu. So besides the natural statistical edge that Venu has, the fact that the highway

news is speculative only increases his chance of benefiting from the agreement

2. Time – There was 6 months time to get clarity on whether the project would fructify

or not.

1. This point actually favors Ajay. Since there is more time to expiry the possibility of the event

working in Ajay’s favor also increases. For example consider this – if you were to run 10kms, in

which time duration are you more likely to achieve it – within 20 mins or within 70 mins?

Obviously higher the time duration higher is the probability to achieve it.

Now let us consider both these points in isolation and figure out the impact it would

have on the option premium.

News – When the deal was done between Ajay and Venu, the news was purely

speculative, hence Venu was happy to accept Rs.100,000/- as premium. However for

a minute assume the news was not speculative and there was some sort of bias.

Maybe there was a local politician who hinted in the recent press conference that

they may consider a highway in that area. With this information, the news is no

longer a rumor. Suddenly there is a possibility that the highway may indeed come

up, albeit there is still an element of speculation.

With this in perspective think about this – do you think Venu will accept Rs.100,000/-

as premium? Maybe not, he knows there is a good chance for the highway to come

up and therefore the land prices would increase. However because there is still an

element of chance he may be willing to take the risk, provided the premium will be

more attractive. Maybe he would consider the agreement attractive if the premium

was Rs.175,000/- instead of Rs.100,000/-.

Now let us put this in stock market perspective. Assume Infosys is trading at

Rs.2200/- today. The 2300 Call option with a 1 month expiry is at Rs.20/-. Put

yourself in Venu’s shoes (option writer) – would you enter into an agreement by

accepting Rs.20/- per share as premium?

If you enter into this options agreement as a writer/seller, then you are giving the

right (to the buyer) of buying Infosys option at Rs. 2300 one month down the lane

from now.

Assume for the next 1 month there is no foreseeable corporate action which will

trigger the share price of Infosys to go higher. Considering this, maybe you may

accept the premium of Rs.20/-.

However what if there is a corporate event (like quarterly results) that tends to

increase the stock price? Will the option seller still go ahead and accept Rs.20/- as

the premium for the agreement? Clearly, it may not be worth to take the risk at

Rs.20/-.

Having said this, what if despite the scheduled corporate event, someone is willing

to offer Rs.75/- as premium instead of Rs.20/-? I suppose at Rs.75/-, it may be worth

taking the risk.

Let us keep this discussion at the back of our mind; we will now take up the 2

point

i.e. ‘time’

When there was 6 months time, clearly Ajay knew that there was ample time for the

dust to settle and the truth to emerge with respect to the highway project. However

instead of 6 months, what if there was only 10 days time? Since the time has shrunk

there is simply not enough time for the event to unfold. Under such a circumstance

(with time not being on Ajay’s side), do you think Ajay will be happy to pay

Rs.100,000/- premium to Venu?. I don’t think so, as there is no incentive for Ajay to

pay that kind of premium to Venu. Maybe he would offer a lesser premium, say

Rs.20,000/- instead.

Anyway, the point that I want to make here keeping both news and time in

perspective is this – premium is never a fixed rate. It is sensitive to several factors.

Some factors tend to increase the premium and some tend to decrease it, and in

real markets, all these factors act simultaneously affecting the premium. To be

precise there are 5 factors (similar to news and time) that tends to affect the

premium. These are called the ‘Option Greeks’. We are too early to understand

Greeks, but will understand the Greeks at a much later stage in this module.

For now, I want you to remember and appreciate the following points with respect

to option premium –

1. The concept of premium is pivotal to the Option Theory

2. Premium is never a fixed rate, it is a function of many (influencing) factors

3. In real markets premiums vary almost on a minute by minute basis

If you have gathered and understood these points so far, I can assure that you are

on the right path.

Options Settlement

Consider this Call option agreement –

As highlighted in green, this is a Call Option to buy JP Associates at Rs.25/-. The

expiry is 26

March 2015. The premium is Rs.1.35/- (highlighted in red), and the

market lot is 8000 shares.

Assume there are 2 traders – ‘Trader A’ and ‘Trader B’. Trader A wants to buy this

agreement (option buyer) and Trader B wants to sell (write) this agreement.

Considering the contract is for 8000 shares, here is how the cash flow would look

like –

Since the premium is Rs.1.35/- per share, Trader A is required to pay the total of

= 8000 * 1.35

= Rs.10,800/- as premium amount to Trader B.

Now because Trader B has received this Premium form Trader A, he is obligated to

sell Trader A 8000 shares of JP Associates on 26

March 2015, if Trader A decides to

exercise his agreement. However, this does not mean that Trader B should have

8000 shares with him on 26

March. Options are cash settled in India, this means on

March, in the event Trader A decides to exercise his right, Trader B is obligated

to pay just the cash differential to Trader A.

To help you understand this better, consider on 26

March JP Associates is trading

at Rs.32/-. This means the option buyer (Trader A) will exercise his right to buy 8000

shares of JP Associates at 25/-. In other words, he is getting to buy JP Associates at

25/- when the same is trading at Rs.32/- in the open market.

Normally, this is how the cash flow should look like –

o On 26

Trader A exercises his right to buy 8000 shares from Trader B

o The price at which the transaction will take place is pre decided at Rs.25 (strike

price)

o Trader A pays Rs.200,000/- (8000 * 25) to Trader B

o Against this payment Trader B releases 8000 shares at Rs.25 to Trader A

o Trader A almost immediately sells these shares in the open market at Rs.32 per

share and receives Rs.256,000/-

o Trader A makes a profit of Rs.56,000/- (256000 – 200000) on this transaction

Another way to look at it is that the option buyer is making a profit of Rs.7/- per

shares (32-25) per share. Because the option is cash settled, instead of giving the

option buyer 8000 shares, the option seller directly gives him the cash equivalent of

the profit he would make. Which means Trader A would receive

= 7*8000

= Rs.56,000/- from Trader B.

Of course, the option buyer had initially spent Rs.10,800/- towards purchasing this

right, hence his real profits would be –

= 56,000 – 10,800

= Rs.45,200/-

In fact if you look at in a percentage return terms, this turns out to be a whopping

return of 419% (without annualizing).

The fact that one can make such large asymmetric return is what makes options an

attractive instrument to trade. This is one of the reasons why Options are massively

popular with traders.

Key takeaways from this chapter

1. It makes sense to buy a call option only when one anticipates an increase in the

price of an asset

2. The strike price is the anchor price at which both the option buyer and option writer

enter into an agreement

3. The underlying price is simply the spot price of the asset

4. Exercising of an option contract is the act of claiming your right to buy the options

contract at the end of the expiry

5. Similar to futures contract, options contract also have an expiry. Option contracts

expire on the last Thursday of every month

6. Option contracts have different expiries – the current month, mid month, and far

month contracts

7. Premiums are not fixed, in fact they vary based on several factors that act upon it

8. Options are cash settled in India.

Module 5 — Options Theory for Professional Trading

Chapter 3

Buying a Call Option

323

3.1 – Buying call option

In the previous chapters we looked at the basic structure of a call option and

understood the broad context under which it makes sense to buy a call option. In

this chapter, we will formally structure our thoughts on the call option and get a

firm understanding on both buying and selling of the call option. Before we move

ahead any further in this chapter, here is a quick recap of what we learnt in the first

chapter –

1. It makes sense to be a buyer of a call option when you expect the underlying price

to increase

2. If the underlying price remains flat or goes down then the buyer of the call option

loses money

3. The money the buyer of the call option would lose is equivalent to the premium

(agreement fees) the buyer pays to the seller/writer of the call option

We will keep the above three points in perspective (which serves as basic guidelines)

and understand the call option to a greater extent.

3.2 – Building a case for a call option

There are many situations in the market that warrants the purchase of a call option.

Here is one that I just discovered while writing this chapter, thought the example

would fit well in the context of our discussions. Have a look at the chart below –

The stock in consideration is Bajaj Auto Limited. As you may know, they are one of

the biggest manufacturers of two wheelers in India. For various reasons the stock

has been beaten down in the market, so much so that the stock is trading at its 52

week low price. I believe there could be an opportunity to initiate a trade here. Here

are my thoughts with respect to this trade –

1. Bajaj Auto is a quality fundamental stock, there is no denying this.

2. The stock has been beaten down so heavily, makes me believe this could be the

market’s over reaction to volatility in Bajaj Auto’s business cycle.

3. I expect the stock price to stop falling sometime soon and eventually rise.

4. However I do not want to buy the stock for delivery (yet) as I’m worried about a

further decline of the stock.

5. Extending the above point, the worry of M2M losses prevents me from buying Bajaj

Auto’s futures as well.

6. At the same time I don’t want to miss an opportunity of a sharp reversal in the stock

price.

To sum up, I’m optimistic on the stock price of Bajaj Auto (the stock price to

eventually increase) but I’m kind of uncertain about the immediate outlook on the

stock. The uncertainty is mainly due the fact that my losses in the short term could

be intense if the weakness in the stock persists. However as per my estimate the

probability of the loss is low, but nevertheless the probability still exists. So what

should I do?

Now, if you realize I’m in a similar dilemma that was Ajay was in (recall the Ajay –

Venu example from chapter 1). A circumstance such as this, builds up for a classic

case of an options trade.

In the context of my dilemma, clearly buying a call option on Bajaj Auto makes sense

for reasons I will explain shortly. Here is a snapshot of Bajaj Auto’s option chain –

As we can see the stock is trading at Rs.2026.9 (highlighted in blue). I will choose to

buy 2050 strike call option by paying a premium of Rs.6.35/- (highlighted in red box

and red arrow). You may be wondering on what basis I choose the 2050 strike price

when in fact there are so many different strike prices available (highlighted in

green)?. Well, the process of strike price selection is a vast topic on its own, we will

eventually get there in this module, but for now let us just believe 2050 is the right

strike price to trade.

3.3 – Intrinsic value of a call option (upon expiry)

So what happens to the call option now considering the expiry is 15 days away?

Well, broadly speaking there are three possible scenarios which I suppose you are

familiar with by now –

Scenario 1 – The stock price goes above the strike price, say 2080

Scenario 2 – The stock price goes below the strike price, say 2030

Scenario 3 – The stock price stays at 2050

The above 3 scenarios are very similar to the ones we had looked at in chapter 1,

hence I will also assume that you are familiar with the P&L calculation at the specific

value of the spot in the given scenarios above (if not, I would suggest you read

through Chapter 1 again).

The idea I’m interested in exploring now is this –

1. You will agree there are only 3 broad scenarios under which the price movement of

Bajaj Auto can be classified (upon expiry) i.e. the price either increases, decreases,

or stays flat

2. But what about all the different prices in between? For example if as per Scenario 1

the price is considered to be at 2080 which is above the strike of 2050. What about

other strike prices such as 2055, 2060, 2065, 2070 etc? Can we generalize anything

here with respect to the P&L?

3. In scenario 2, the price is considered to be at 2030 which is below the strike of 2050.

What about other strike prices such as 2045, 2040, 2035 etc? Can we generalize

anything here with respect to the P&L?

What would happen to the P&L at various possible prices of spot (upon expiry) – I

would like to call these points as the “Possible values of the spot on expiry” and sort

of generalize the P&L understanding of the call option.

In order to do this, I would like to first talk about (in part and not the full concept)

the idea of the ‘intrinsic value of the option upon expiry’.

The intrinsic value (IV) of the option upon expiry (specifically a call option for now)

is defined as the non – negative value which the option buyer is entitled to if he

were to exercise the call option. In simple words ask yourself (assuming you are the

buyer of a call option) how much money you would receive upon expiry, if the call

option you hold is profitable. Mathematically it is defined as –

IV = Spot Price – Strike Price

So if Bajaj Auto on the day of expiry is trading at 2068 (in the spot market) the 2050

Call option’s intrinsic value would be –

= 2068 – 2050

= 18

Likewise, if Bajaj Auto is trading at 2025 on the expiry day the intrinsic value of the

option would be –

= 2025 – 2050

= -25

But remember, IV of an option (irrespective of a call or put) is a non negative

number; hence we leave the IV at 2025

= 0

Now our objective is to keep the idea of intrinsic value of the option in perspective,

and to identify how much money I will make at every possible expiry value of Bajaj

Auto and in the process make some generalizations on the call option buyer’s P&L.

3.4 – Generalizing the P&L for a call option buyer

Now keeping the concept of intrinsic value of an option at the back of our mind, let

us work towards building a table which would help us identify how much money, I

as the buyer of Bajaj Auto’s 2050 call option would make under the various possible

spot value changes of Bajaj Auto (in spot market) on expiry. Do remember the

premium paid for this option is Rs 6.35/–. Irrespective of how the spot value

changes, the fact that I have paid Rs.6.35/- remains unchanged. This is the cost that I

have incurred in order to buy the 2050 Call Option. Let us keep this in perspective

and work out the P&L table –

Please note – the negative sign before the premium paid represents a cash out flow from

my trading account.

Serial No.

Possible values of spot

Premium Paid

Intrinsic Value (IV)

P&L (IV + Premium)

1990

(-) 6.35

1990 – 2050 = 0

= 0 + (– 6.35) = – 6.35

2000

(-) 6.35

2000 – 2050 = 0

= 0 + (– 6.35) = – 6.35

2010

(-) 6.35

2010 – 2050 = 0

= 0 + (– 6.35) = – 6.35

2020

(-) 6.35

2020 – 2050 = 0

= 0 + (– 6.35) = – 6.35

2030

(-) 6.35

2030 – 2050 = 0

= 0 + (– 6.35) = – 6.35

2040

(-) 6.35

2040 – 2050 = 0

= 0 + (– 6.35) = – 6.35

2050

(-) 6.35

2050 – 2050 = 0

= 0 + (– 6.35) = – 6.35

2060

(-) 6.35

2060 – 2050 = 10

= 10 +(-6.35) = + 3.65

2070

(-) 6.35

2070 – 2050 = 20

= 20 +(-6.35) = + 13.65

2080

(-) 6.35

2080 – 2050 = 30

= 30 +(-6.35) = + 23.65

2090

(-) 6.35

2090 – 2050 = 40

= 40 +(-6.35) = + 33.65

2100

(-) 6.35

2100 – 2050 = 50

= 50 +(-6.35) = + 43.65

So what do you observe? The table above throws out 2 strong observations –

1. Even if the price of Bajaj Auto goes down (below the strike price of 2050), the

maximum loss seems to be just Rs.6.35/-

1. Generalization 1 – For a call option buyer a loss occurs when the spot price moves below the

strike price. However the loss to the call option buyer is restricted to the extent of the premium

he has paid

2. The profit from this call option seems to increase exponentially as and when Bajaj

Auto starts to move above the strike price of 2050

1. Generalization 2 – The call option becomes profitable as and when the spot price moves over

and above the strike price. The higher the spot price goes from the strike price, the higher the

profit.

3. From the above 2 generalizations it is fair for us to say that the buyer of the call

option has a limited risk and a potential to make an unlimited profit.

Here is a general formula that tells you the Call option P&L for a given spot price –

P&L = Max [0, (Spot Price – Strike Price)] – Premium Paid

Going by the above formula, let’s evaluate the P&L for a few possible spot values on

expiry –

1. 2023

2. 2072

3. 2055

The solution is as follows –

@2023

= Max [0, (2023 – 2050)] – 6.35

= Max [0, (-27)] – 6.35

= 0 – 6.35

= – 6.35

The answer is in line with Generalization 1 (loss restricted to the extent of premium

paid).

@2072

= Max [0, (2072 – 2050)] – 6.35

= Max [0, (+22)] – 6.35

= 22 – 6.35

= +15.65

The answer is in line with Generalization 2 (Call option gets profitable as and when

the spot price moves over and above the strike price).

@2055

= Max [0, (2055 – 2050)] – 6.35

= Max [0, (+5)] – 6.35

= 5 – 6.35

= -1.35

So, here is a tricky situation, the result what we obtained here is against the

generalization. Despite the spot price being above the strike price, the trade is

resulting in a loss! Why is this so? Also if you observe the loss is much lesser than

the maximum loss of Rs.6.35/-, it is in fact just Rs.1.35/-. To understand why this is

happening we should diligently inspect the P&L behavior around the spot value

which is slightly above the strike price (2050 in this case).

Serial No.

Possible values of spot

Premium Paid

Intrinsic Value (IV)

P&L (IV + Premium)

2050

(-) 6.35

2050 – 2050 = 0

= 0 + (– 6.35) = – 6.35

2051

(-) 6.35

2051 – 2050 = 1

= 1 + (– 6.35) = – 5.35

2052

(-) 6.35

2052 – 2050 = 2

= 2 + (– 6.35) = – 4.35

2053

(-) 6.35

2053 – 2050 = 3

= 3 + (– 6.35) = – 3.35

2054

(-) 6.35

2054 – 2050 = 4

= 4 + (– 6.35) = – 2.35

2055

(-) 6.35

2055 – 2050 = 5

= 5 + (– 6.35) = – 1.35

2056

(-) 6.35

2056 – 2050 = 6

= 6 + (– 6.35) = – 0.35

2057

(-) 6.35

2057 – 2050 = 7

= 7 +(- 6.35) = + 0.65

2058

(-) 6.35

2058 – 2050 = 8

= 8 +(- 6.35) = + 1.65

2059

(-) 6.35

2059 – 2050 = 9

= 9 +(- 6.35) = + 2.65

As you notice from the table above, the buyer suffers a maximum loss (Rs. 6.35 in

this case) till the spot price is equal to the strike price. However, when the spot price

starts to move above the strike price, the loss starts to minimize. The losses keep

getting minimized till a point where the trade neither results in a profit or a loss.

This is called the breakeven point.

The formula to identify the breakeven point for any call option is –

B.E = Strike Price + Premium Paid

For the Bajaj Auto example, the ‘Break Even’ point is –

= 2050 + 6.35

= 2056.35

In fact let us find out find out the P&L at the breakeven point

= Max [0, (2056.35 – 2050)] – 6.35

= Max [0, (+6.35)] – 6.35

= +6.35 – 6.35

= 0

As you can see, at the breakeven point we neither make money nor lose money. In

other words, if the call option has to be profitable it not only has to move above the

strike price but it has to move above the breakeven point.

3.5 – Call option buyer’s payoff

So far we have understood a few very important features with respect to a call

option buyer’s payoff; I will reiterate the same –

1. The maximum loss the buyer of a call option experiences is, to the extent of the

premium paid. The buyer experiences a loss as long as the spot price is below the

strike price

2. The call option buyer has the potential to realize unlimited profits provided the spot

price moves higher than the strike price

3. Though the call option is supposed to make a profit when the spot price moves

above the strike price, the call option buyer first needs to recover the premium he

has paid

4. The point at which the call option buyer completely recovers the premium he has

paid is called the breakeven point

5. The call option buyer truly starts making a profit only beyond the breakeven point

(which naturally is above the strike price)

Interestingly, all these points can be visualized if we plot the chart of the P&L. Here

is the P&L chart of Bajaj Auto’s Call Option trade –

From the chart above you can notice the following points which are in line with the

discussion we have just had –

1. The loss is restricted to Rs.6.35/- as long as the spot price is trading at any price

below the strike of 2050

2. From 2050 to 2056.35 (breakeven price) we can see the losses getting minimized

3. At 2056.35 we can see that there is neither a profit nor a loss

4. Above 2056.35 the call option starts making money. In fact the slope of the P&L line

clearly indicates that the profits start increasing exponentially as and when the spot

value moves away from the strike

Again, from the graph one thing is very evident – A call option buyer has a limited

risk but unlimited profit potential. And with this I hope you are now clear with the

call option from the buyer’s perspective. In the next chapter we will look into the Call

Option from the seller’s perspective.

Key takeaways from this chapter

1. It makes sense to be a buyer of a call option when you expect the underlying price

to increase

2. If the underlying price remains flat or goes down then the buyer of the call option

loses money

3. The money the buyer of the call option would lose is equivalent to the premium

(agreement fees) the buyer pays to the seller/writer of the call option

4. Intrinsic value (IV) of a call option is a non negative number

5. IV = Max[0, (spot price – strike price)]

6. The maximum loss the buyer of a call option experiences is to the extent of the

premium paid. The loss is experienced as long as the spot price is below the strike

price

7. The call option buyer has the potential to make unlimited profits provided the spot

price moves higher than the strike price

8. Though the call option is supposed to make a profit when the spot price moves

above the strike price, the call option buyer first needs to recover the premium he

has paid

9. The point at which the call option buyer completely recovers the premium he has

paid is called the breakeven point

10. The call option buyer truly starts making a profit only beyond the breakeven point

(which naturally is above the strike price).

Module 5 — Options Theory for Professional Trading

Chapter 4

Selling/Writing a Call Option

458

4.1 – Two sides of the same coin

Do you remember the 1975 Bollywood super hit flick ‘Deewaar’, which attained a

cult status for the incredibly famous ‘Mere paas maa hai’ dialogue ? The movie

is about two brothers from the same mother. While one brother, righteous in life

grows up to become a cop, the other brother turns out to be a notorious criminal

whose views about life is diametrically opposite to his cop brother.

Well, the reason why I’m taking about this legendary movie now is that the option

writer and the option buyer are somewhat comparable to these brothers. They are

the two sides of the same coin. Of course, unlike the Deewaar brothers there is no

view on morality when it comes to Options trading; rather the view is more on

markets and what one expects out of the markets. However, there is one thing that

you should remember here – whatever happens to the option seller in terms of the

P&L, the exact opposite happens to option buyer and vice versa. For example if the

option writer is making Rs.70/- in profits, this automatically means the option buyer

is losing Rs.70/-. Here is a quick list of such generalisations –

o If the option buyer has limited risk (to the extent of premium paid), then the option

seller has limited profit (again to the extent of the premium he receives)

o If the option buyer has unlimited profit potential then the option seller potentially

has unlimited risk

o The breakeven point is the point at which the option buyer starts to make money,

this is the exact same point at which the option writer starts to lose money

o If option buyer is making Rs.X in profit, then it implies the option seller is making a

loss of Rs.X

o If the option buyer is losing Rs.X, then it implies the option seller is making Rs.X in

profits

o Lastly if the option buyer is of the opinion that the market price will increase (above

the strike price to be particular) then the option seller would be of the opinion that

the market will stay at or below the strike price…and vice versa.

To appreciate these points further it would make sense to take a look at the Call

Option from the seller’s perspective, which is the objective of this chapter.

Before we proceed, I have to warn you something about this chapter – since there is

P&L symmetry between the option seller and the buyer, the discussion going

forward in this chapter will look very similar to the discussion we just had in the

previous chapter, hence there is a possibility that you could just skim through the

chapter. Please don’t do that, I would suggest you stay alert to notice the subtle

difference and the huge impact it has on the P&L of the call option writer.

4.2 – Call option seller and his thought process

Recall the ‘Ajay-Venu’ real estate example from chapter 1 – we discussed 3 possible

scenarios that would take the agreement to a logical conclusion –

1. The price of the land moves above Rs.500,000 (good for Ajay – option buyer)

2. The price stays flat at Rs.500,000 (good for Venu – option seller)

3. The price moves lower than Rs.500,000 (good for Venu – option seller)

If you notice, the option buyer has a statistical disadvantage when he buys options

– only 1 possible scenario out of the three benefits the option buyer. In other words

2 out of the 3 scenarios benefit the option seller. This is just one of the incentives

for the option writer to sell options. Besides this natural statistical edge, if the

option seller also has a good market insight then the chances of the option seller

being profitable are quite high.

Please do note, I’m only talking about a natural statistical edge here and by no way

am I suggesting that an option seller will always make money.

Anyway let us now take up the same ‘Bajaj Auto’ example we took up in the previous

chapter and build a case for a call option seller and understand how he would view

the same situation. Allow me repost the chart –

o The stock has been heavily beaten down, clearly the sentiment is extremely weak

o Since the stock has been so heavily beaten down – it implies many investors/traders

in the stock would be stuck in desperate long positions

o Any increase in price in the stock will be treated as an opportunity to exit from the

stuck long positions

o Given this, there is little chance that the stock price will increase in a hurry –

especially in the near term

o Since the expectation is that the stock price won’t increase, selling the Bajaj Auto’s

call option and collecting the premium can be perceived as a good trading

opportunity

With these thoughts, the option writer decides to sell a call option. The most

important point to note here is – the option seller is selling a call option because he

believes that the price of Bajaj Auto will NOT increase in the near future. Therefore

he believes that, selling the call option and collecting the premium is a good

strategy.

As I mentioned in the previous chapter, selecting the right strike price is a very

important aspect of options trading. We will talk about this in greater detail as we go

forward in this module. For now, let us assume the option seller decides to sell Bajaj

Auto’s 2050 strike option and collect Rs.6.35/- as premiums. Please refer to the

option chain below for the details –

Let us now run through the same exercise that we ran through in the previous

chapter to understand the P&L profile of the call option seller and in the process

make the required generalizations. The concept of an intrinsic value of the option

that we discussed in the previous chapter will hold true for this chapter as well.

Serial No.

Possible values of spot

Premium Received

Intrinsic Value (IV)

P&L (Premium – IV)

1990

+ 6.35

1990 – 2050 = 0

= 6.35 – 0 = + 6.35

2000

+ 6.35

2000 – 2050 = 0

= 6.35 – 0 = + 6.35

2010

+ 6.35

2010 – 2050 = 0

= 6.35 – 0 = + 6.35

2020

+ 6.35

2020 – 2050 = 0

= 6.35 – 0 = + 6.35

2030

+ 6.35

2030 – 2050 = 0

= 6.35 – 0 = + 6.35

2040

+ 6.35

2040 – 2050 = 0

= 6.35 – 0 = + 6.35

2050

+ 6.35

2050 – 2050 = 0

= 6.35 – 0 = + 6.35

2060

+ 6.35

2060 – 2050 = 10

= 6.35 – 10 = – 3.65

2070

+ 6.35

2070 – 2050 = 20

= 6.35 – 20 = – 13.65

2080

+ 6.35

2080 – 2050 = 30

= 6.35 – 30 = – 23.65

2090

+ 6.35

2090 – 2050 = 40

= 6.35 – 40 = – 33.65

2100

+ 6.35

2100 – 2050 = 50

= 6.35 – 50 = – 43.65

Before we proceed to discuss the table above, please note –

1. The positive sign in the ‘premium received’ column indicates a cash inflow (credit) to

the option writer

2. The intrinsic value of an option (upon expiry) remains the same irrespective of

call option buyer or seller

3. The net P&L calculation for an option writer changes slightly, the logic goes like this

1. When an option seller sells options he receives a premium (for example Rs.6.35/).

He would experience a loss only after he losses the entire premium. Meaning after

receiving a premium of Rs.6.35, if he loses Rs.5/- it implies he is still in profit of

Rs.1.35/-. Hence for an option seller to experience a loss he has to first lose the

premium he has received, any money he loses over and above the premium

received, will be his real loss. Hence the P&L calculation would be ‘Premium –

Intrinsic Value’

2. You can extend the same argument to the option buyer. Since the option buyer

pays a premium, he first needs to recover the premium he has paid, hence he

would be profitable over and above the premium amount he has received, hence

the P&L calculation would be ‘ Intrinsic Value – Premium’.

The table above should be familiar to you now. Let us inspect the table and make a

few generalizations (do bear in mind the strike price is 2050) –

1. As long as Bajaj Auto stays at or below the strike price of 2050, the option seller gets

to make money – as in he gets to pocket the entire premium of Rs.6.35/-. However,

do note the profit remains constant at Rs.6.35/-.

1. Generalization 1 – The call option writer experiences a maximum profit to the extent of the

premium received as long as the spot price remains at or below the strike price (for a call option)

2. The option writer experiences an exponential loss as and when Bajaj Auto starts to

move above the strike price of 2050

1. Generalization 2 – The call option writer starts to lose money as and when the spot price moves

over and above the strike price. Higher the spot price moves away from the strike price, larger

the loss.

3. From the above 2 generalizations it is fair to conclude that, the option seller can

earn limited profits and can experience unlimited loss

We can put these generalizations in a formula to estimate the P&L of a Call option

seller –

P&L = Premium – Max [0, (Spot Price – Strike Price)]

Going by the above formula, let’s evaluate the P&L for a few possible spot values on

expiry –

1. 2023

2. 2072

3. 2055

The solution is as follows –

@2023

= 6.35 – Max [0, (2023 – 2050)]

= 6.35 – Max [0, -27]

= 6.35 – 0

= 6.35

The answer is in line with Generalization 1 (profit restricted to the extent of

premium received).

@2072

= 6.35 – Max [0, (2072 – 2050)]

= 6.35 – 22

= -15.56

The answer is in line with Generalization 2 (Call option writers would experience a

loss as and when the spot price moves over and above the strike price)

@2055

= 6.35 – Max [0, (2055 – 2050)]

= 6.35 – Max [0, +5]

= 6.35 – 5

= 1.35

Though the spot price is higher than the strike, the call option writer still seems to

be making some money here. This is against the 2

generalization. I’m sure you

would know this by now, this is because of the ‘breakeven point’ concept, which we

discussed in the previous chapter.

Anyway let us inspect this a bit further and look at the P&L behavior in and around

the strike price to see exactly at which point the option writer will start making a

loss.

Serial No.

Possible values of spot

Premium Received

Intrinsic Value (IV)

P&L (Premium – IV)

2050

+ 6.35

2050 – 2050 = 0

= 6.35 – 0 = 6.35

2051

+ 6.35

2051 – 2050 = 1

= 6.35 – 1 = 5.35

2052

+ 6.35

2052 – 2050 = 2

= 6.35 – 2 = 4.35

2053

+ 6.35

2053 – 2050 = 3

= 6.35 – 3 = 3.35

2054

+ 6.35

2054 – 2050 = 4

= 6.35 – 4 = 2.35

2055

+ 6.35

2055 – 2050 = 5

= 6.35 – 5 = 1.35

2056

+ 6.35

2056 – 2050 = 6

= 6.35 – 6 = 0.35

2057

+ 6.35

2057 – 2050 = 7

= 6.35 – 7 = – 0.65

2058

+ 6.35

2058 – 2050 = 8

= 6.35 – 8 = – 1.65

2059

+ 6.35

2059 – 2050 = 9

= 6.35 – 9 = – 2.65

Clearly even when the spot price moves higher than the strike, the option writer still

makes money, he continues to make money till the spot price increases more

than strike + premium received. At this point he starts to lose money, hence calling

this the ‘breakdown point’ seems appropriate.

Breakdown point for the call option seller = Strike Price + Premium Received

For the Bajaj Auto example,

= 2050 + 6.35

= 2056.35

So, the breakeven point for a call option buyer becomes the breakdown point for

the call option seller.

4.3 – Call Option seller pay-off

As we have seen throughout this chapter, there is a great symmetry between the

call option buyer and the seller. In fact the same can be observed if we plot the P&L

graph of an option seller. Here is the same –

The call option sellers P&L payoff looks like a mirror image of the call option buyer’s

P&L pay off. From the chart above you can notice the following points which are in

line with the discussion we have just had –

1. The profit is restricted to Rs.6.35/- as long as the spot price is trading at any price

below the strike of 2050

2. From 2050 to 2056.35 (breakdown price) we can see the profits getting minimized

3. At 2056.35 we can see that there is neither a profit nor a loss

4. Above 2056.35 the call option seller starts losing money. In fact the slope of the P&L

line clearly indicates that the losses start to increase exponentially as and when the

spot value moves away from the strike price

4.4 – A note on margins

Think about the risk profile of both the call option buyer and a call option seller. The

call option buyer bears no risk. He just has to pay the required premium amount to

the call option seller, against which he would buy the right to buy the underlying at

a later point. We know his risk (maximum loss) is restricted to the premium he has

already paid.

However when you think about the risk profile of a call option seller, we know that

he bears an unlimited risk. His potential loss can exponentially increase as and

when the spot price moves above the strike price. Having said this, think about the

stock exchange – how can they manage the risk exposure of an option seller in the

backdrop of an ‘unlimited loss’ potential? What if the loss becomes so huge that the

option seller decides to default?

Clearly the stock exchange cannot afford to permit a derivative participant to carry

such a huge default risk, hence it is mandatory for the option seller to park some

money as margins. The margins charged for an option seller is similar to the margin

requirement for a futures contract.

Here is the snapshot from the Zerodha Margin calculator for Bajaj Auto futures and

Bajaj Auto 2050 Call option, both expiring on 30

April 2015.

And here is the margin requirement for selling 2050 call option.

As you can see the margin requirements are somewhat similar in both the cases

(option writing and trading futures). Of course there is a small difference; we will

deal with it at a later stage. For now, I just want you to note that option selling

requires margins similar to futures trading, and the margin amount is roughly the

same.

4.5 – Putting things together

I hope the last four chapters have given you all the clarity you need with respect to

call options buying and selling. Unlike other topics in Finance, options are a little

heavy duty. Hence I guess it makes sense to consolidate our learning at every

opportunity and then proceed further. Here are the key things you should

remember with respect to buying and selling call options.

With respect to option buying

o You buy a call option only when you are bullish about the underlying asset. Upon

expiry the call option will be profitable only if the underlying has moved over and

above the strike price

o Buying a call option is also referred to as ‘Long on a Call Option’ or simply ‘Long Call’

o To buy a call option you need to pay a premium to the option writer

o The call option buyer has limited risk (to the extent of the premium paid) and an

potential to make an unlimited profit

o The breakeven point is the point at which the call option buyer neither makes

money nor experiences a loss

o P&L = Max [0, (Spot Price – Strike Price)] – Premium Paid

o Breakeven point = Strike Price + Premium Paid

With respect to option selling

o You sell a call option (also called option writing) only when you believe that upon

expiry, the underlying asset will not increase beyond the strike price

o Selling a call option is also called ‘Shorting a call option’ or simply ‘Short Call’

o When you sell a call option you receive the premium amount

o The profit of an option seller is restricted to the premium he receives, however his

loss is potentially unlimited

o The breakdown point is the point at which the call option seller gives up all the

premium he has made, which means he is neither making money nor is losing

money

o Since short option position carries unlimited risk, he is required to deposit margin

o Margins in case of short options is similar to futures margin

o P&L = Premium – Max [0, (Spot Price – Strike Price)]

o Breakdown point = Strike Price + Premium Received

Other important points

o When you are bullish on a stock you can either buy the stock in spot, buy its futures,

or buy a call option

o When you are bearish on a stock you can either sell the stock in the spot (although

on a intraday basis), short futures, or short a call option

o The calculation of the intrinsic value for call option is standard, it does not change

based on whether you are an option buyer/ seller

o However the intrinsic value calculation changes for a ‘Put’ option

o The net P&L calculation methodology is different for the call option buyer and seller.

o Throughout the last 4 chapters we have looked at the P&L keeping the expiry in

perspective, this is only to help you understand the P&L behavior better

o One need not wait for the option expiry to figure out if he is going to be profitable

or not

o Most of the option trading is based on the change in premiums

o For example, if I have bought Bajaj Auto 2050 call option at Rs.6.35 in the morning

and by noon the same is trading at Rs.9/- I can choose to sell and book profits

o The premiums change dynamically all the time, it changes because of many

variables at play, we will understand all of them as we proceed through this module

o Call option is abbreviated as ‘CE’. So Bajaj Auto 2050 Call option is also referred to as

Bajaj Auto 2050CE. CE is an abbreviation for ‘European Call Option’.

4.6 – European versus American Options

Initially when option was introduced in India, there are two types of options

available – European and American Options. All index options (Nifty, Bank Nifty

options) were European in nature and the stock options were American in nature.

The difference between the two was mainly in terms of ‘Options exercise’.

European Options – If the option type is European then it means that the option

buyer will have to mandatory wait till the expiry date to exercise his right. The

settlement is based on the value of spot market on expiry day. For example if

he has bought a Bajaj Auto 2050 Call option, then for the buyer to be profitable

Bajaj Auto has to go higher than the breakeven point on the day of the expiry. Even

not it the option is worthless to the buyer and he will lose all the premium money

that he paid to the Option seller.

American Options – In an American Option, the option buyer can exercise his right

to buy the option whenever he deems appropriate during the tenure of the options

expiry. The settlement is dependent of the spot market at that given moment

and not really depended on expiry. For instance he buys Bajaj Auto 2050 Call

option today when Bajaj is trading at 2030 in spot market and there are 20 more

days for expiry. The next day Bajaj Auto crosses 2050. In such a case, the buyer of

Baja Auto 2050 American Call option can exercise his right, which means the seller is

obligated to settle with the option buyer. The expiry date has little significance here.

For people familiar with option you may have this question – ‘Since we can anyway

buy an option now and sell it later, maybe in 30 minutes after we purchase, how

does it matter if the option is American or European?’.

Valid question, well think about the Ajay-Venu example again. Here Ajay and Venu

were to revisit the agreement in 6 months time (this is like a European Option). If

instead of 6 months, imagine if Ajay had insisted that he could come anytime during

the tenure of the agreement and claim his right (like an American Option). For

example there could be a strong rumor about the highway project (after they signed

off the agreement). In the back of the strong rumor, the land prices shoots up and

hence Ajay decides exercise his right, clearly Venu will be obligated to deliver the

land to Ajay (even though he is very clear that the land price has gone up because of

strong rumors). Now because Venu carries addition risk of getting ‘exercised’ on any

day as opposed to the day of the expiry, the premium he would need is also higher

(so that he is compensated for the risk he takes).

For this reason, American options are always more expensive than European

Options.

Also, you maybe interested to know that about 3 years ago NSE decided to get rid of

American option completely from the derivatives segment. So all options in India

are now European in nature, which means the buyer can exercise his option

based on the spot price on the expiry day.

We will now proceed to understand the ‘Put Options’.

Key takeaways from this chapter

1. You sell a call option when you are bearish on a stock

2. The call option buyer and the seller have a symmetrically opposite P&L behavior

3. When you sell a call option you receive a premium

4. Selling a call option requires you to deposit a margin

5. When you sell a call option your profit is limited to the extent of the premium you

receive and your loss can potentially be unlimited

6. P&L = Premium – Max [0, (Spot Price – Strike Price)]

7. Breakdown point = Strike Price + Premium Recieved

8. In India all options are European in nature

Module 5 — Options Theory for Professional Trading

Chapter 5

The Put Option Buying

103

5.1 – Getting the orientation right

I hope by now you are through with the practicalities of a Call option from both the

buyers and sellers perspective. If you are indeed familiar with the call option then

orienting yourself to understand ‘Put Options’ is fairly easy. The only change in a

put option (from the buyer’s perspective) is the view on markets should be bearish

as opposed to the bullish view of a call option buyer.

The put option buyer is betting on the fact that the stock price will go down (by the

time expiry approaches). Hence in order to profit from this view he enters into a Put

Option agreement. In a put option agreement, the buyer of the put option can buy

the right to sell a stock at a price (strike price) irrespective of where the

underlying/stock is trading at.

Remember this generality – whatever the buyer of the option anticipates, the seller

anticipates the exact opposite, therefore a market exists. After all, if everyone

expects the same a market can never exist. So if the Put option buyer expects the

market to go down by expiry, then the put option seller would expect the market (or

the stock) to go up or stay flat.

A put option buyer buys the right to sell the underlying to the put option writer at

a predetermined rate (Strike price. This means the put option seller, upon expiry will

have to buy if the ‘put option buyer’ is selling him. Pay attention here – at the time

of the agreement the put option seller is selling a right to the put option buyer

where in the buyer can ‘sell’ the underlying to the ‘put option seller’ at the time of

expiry.

Confusing? well, just think of the ‘Put Option’ as a simple contract where two parties

meet today and agree to enter into a transaction based on the price of an

underlying –

o The party agreeing to pay a premium is called the ‘contract buyer’ and the party

receiving the premium is called the ‘contract seller’

o The contract buyer pays a premium and buys himself a right

o The contract seller receives the premium and obligates himself

o The contract buyer will decide whether or not to exercise his right on the expiry day

o If the contract buyer decides to exercise his right then he gets to sell the underlying

(maybe a stock) at the agreed price (strike price) and the contract seller will be

obligated to buy this underlying from the contract buyer

o Obviously the contract buyer will exercise his right only if the underlying price is

trading below the strike price – this means by virtue of the contract the buyer holds,

he can sell the underlying at a much higher price to the contract seller when the

same underlying is trading at a lower price in the open market.

Still confusing? Fear not, we will deal with an example to understand this more

clearly.

Consider this situation, between the Contract buyer and the Contract seller –

o Assume Reliance Industries is trading at Rs.850/-

o Contract buyer buys the right to sell Reliance to contract seller at Rs.850/- upon

expiry

o To obtain this right, contract buyer has to pay a premium to the contract seller

o Against the receipt of the premium contract seller will agree to buy Reliance

Industries shares at Rs.850/- upon expiry but only if contract buyer wants him to

buy it from him

o For example if upon expiry Reliance is at Rs.820/- then contract buyer can demand

contract seller to buy Reliance at Rs.850/- from him

o This means contract buyer can enjoy the benefit of selling Reliance at Rs.850/- when

it is trading at a lower price in the open market (Rs.820/-)

o If Reliance is trading at Rs.850/- or higher upon expiry (say Rs.870/-) it does not

make sense for contract buyer to exercise his right and ask contract seller to buy

the shares from him at Rs.850/-. This is quite obvious since he can sell it at a higher

rate in the open market

o A agreement of this sort where one obtains the right to sell the underlying asset

upon expiry is called a ‘Put option’

o Contract seller will be obligated to buy Reliance at Rs.850/- from contract buyer

because he has sold Reliance 850 Put Option to contract buyer

I hope the above discussion has given you the required orientation to the Put

Options. If you are still confused, it is alright as I’m certain you will develop more

clarity as we proceed further. However there are 3 key points you need to be aware

of at this stage –

o The buyer of the put option is bearish about the underlying asset, while the seller of

the put option is neutral or bullish on the same underlying

o The buyer of the put option has the right to sell the underlying asset upon expiry at

the strike price

o The seller of the put option is obligated (since he receives an upfront premium) to

buy the underlying asset at the strike price from the put option buyer if the buyer

wishes to exercise his right.

5.2 – Building a case for a Put Option buyer

Like we did with the call option, let us build a practical case to understand the put

option better. We will first deal with the Put Option from the buyer’s perspective

and then proceed to understand the put option from the seller’s perspective.

Here is the end of day chart of Bank Nifty (as on 8

April 2015) –

Here are some of my thoughts with respect to Bank Nifty –

1. Bank Nifty is trading at 18417

2. 2 days ago Bank Nifty tested its resistance level of 18550 (resistance level

highlighted by a green horizontal line)

3. I consider 18550 as resistance since there is a price action zone at this level which is

well spaced in time (for people who are not familiar with the concept of resistance I

would suggest you read about it here

4. I have highlighted the price action zone in a blue rectangular boxes

5. On 7

of April (yesterday) RBI maintained a status quo on the monetary rates – they

kept the key central bank rates unchanged (as you may know RBI monetary policy is

the most important event for Bank Nifty)

6. Hence in the backdrop of a technical resistance and lack of any key fundamental

trigger, banks may not be the flavor of the season in the markets

7. As result of which traders may want to sell banks and buy something else which is

the flavor of the season

8. For these reasons I have a bearish bias towards Bank Nifty

9. However shorting futures maybe a bit risky as the overall market is bullish, it is only

the banking sector which is lacking luster

10. Under circumstances such as these employing an option is best, hence buying a Put

Option on the bank Nifty may make sense

11. Remember when you buy a put option you benefit when the underlying goes down

Backed by this reasoning, I would prefer to buy the 18400 Put Option which is

trading at a premium of Rs.315/-. Remember to buy this 18400 Put option, I will

have to pay the required premium (Rs.315/- in this case) and the same will be

received by the 18400 Put option seller.

Of course buying the Put option is quite simple – the easiest way is to call your

broker and ask him to buy the Put option of a specific stock and strike and it will be

done for you in matter of a few seconds. Alternatively you can buy it yourself

through a trading terminal such as Zerodha Pi We will get into the technicalities of

buying and selling options via a trading terminal at a later stage.

Now assuming I have bought Bank Nifty’s 18400 Put Option, it would be interesting

to observe the P&L behavior of the Put Option upon its expiry. In the process we

can even make a few generalizations about the behavior of a Put option’s P&L.

5.3 – Intrinsic Value (IV) of a Put Option

Before we proceed to generalize the behavior of the Put Option P&L, we need to

understand the calculation of the intrinsic value of a Put option. We discussed the

concept of intrinsic value in the previous chapter; hence I will assume you know the

concept behind IV. Intrinsic Value represents the value of money the buyer will

receive if he were to exercise the option upon expiry.

The calculation for the intrinsic value of a Put option is slightly different from that of

a call option. To help you appreciate the difference let me post here the intrinsic

value formula for a Call option –

IV (Call option) = Spot Price – Strike Price

The intrinsic value of a Put option is –

IV (Put Option) = Strike Price – Spot Price

I want you to remember an important aspect here with respect to the intrinsic value

of an option – consider the following timeline –

The formula to calculate the intrinsic value of an option that we have just looked at,

is applicable only on the day of the expiry. However the calculation of intrinsic

value of an option is different during the series. Of course we will understand how

to calculate (and the need to calculate) the intrinsic value of an option during the

expiry. But for now, we only need to know the calculation of the intrinsic value upon

expiry.

5.4 – P&L behavior of the Put Option buyer

Keeping the concept of intrinsic value of a put option at the back of our mind, let us

work towards building a table which would help us identify how much money, I as

the buyer of Bank Nifty’s 18400 put option would make under the various possible

spot value changes of Bank Nifty (in spot market) on expiry. Do remember the

premium paid for this option is Rs 315/–. Irrespective of how the spot value

changes, the fact that I have paid Rs.315/- will remain unchanged. This is the cost

that I have incurred in order to buy the Bank Nifty 18400 Put Option. Let us keep

this in perspective and work out the P&L table –

Please note – the negative sign before the premium paid represents a cash outflow from

my trading account.

Serial No.

Possible values of spot

Premium Paid

Intrinsic Value (IV)

P&L (IV + Premium)

16195

-315

18400 – 16195 = 2205

2205 + (-315) = + 1890

16510

-315

18400 – 16510 = 1890

1890 + (-315)= + 1575

16825

-315

18400 – 16825 = 1575

1575 + (-315) = + 1260

17140

-315

18400 – 17140 = 1260

1260 + (-315) = + 945

17455

-315

18400 – 17455 = 945

945 + (-315) = + 630

17770

-315

18400 – 17770 = 630

630 + (-315) = + 315

18085

-315

18400 – 18085 = 315

315 + (-315) = 0

18400

-315

18400 – 18400 = 0

0 + (-315)= – 315

18715

-315

18400 – 18715 = 0

0 + (-315) = -315

19030

-315

18400 – 19030 = 0

0 + (-315) = -315

19345

-315

18400 – 19345 = 0

0 + (-315) = -315

19660

-315

18400 – 19660 = 0

0 + (-315) = -315

Let us make some observations on the behavior of the P&L (and also make a few

P&L generalizations). For the above discussion, set your eyes at row number 8 as

your reference point –

1. The objective behind buying a put option is to benefit from a falling price. As we can

see, the profit increases as and when the price decreases in the spot market (with

reference to the strike price of 18400).

1. Generalization 1 – Buyers of Put Options are profitable as and when the spot price

goes below the strike price. In other words buy a put option only when you are

bearish about the underlying

2. As the spot price goes above the strike price (18400) the position starts to make a

loss. However the loss is restricted to the extent of the premium paid, which in this

case is Rs.315/-

1. Generalization 2 – A put option buyer experiences a loss when the spot price goes

higher than the strike price. However the maximum loss is restricted to the extent

of the premium the put option buyer has paid.

Here is a general formula using which you can calculate the P&L from a Put Option

position. Do bear in mind this formula is applicable on positions held till expiry.

P&L = [Max (0, Strike Price – Spot Price)] – Premium Paid

Let us pick 2 random values and evaluate if the formula works –

1. 16510

2. 19660

@16510 (spot below strike, position has to be profitable)

= Max (0, 18400 -16510)] – 315

= 1890 – 315

= + 1575

@19660 (spot above strike, position has to be loss making, restricted to premium

paid)

= Max (0, 18400 – 19660) – 315

= Max (0, -1260) – 315

= – 315

Clearly both the results match the expected outcome.

Further, we need to understand the breakeven point calculation for a Put Option

buyer. Note, I will take the liberty of skipping the explanation of a breakeven point

as we have already dealt with it in the previous chapter; hence I will give you the

formula to calculate the same –

Breakeven point = Strike Price – Premium Paid

For the Bank Nifty breakeven point would be

= 18400 – 315

= 18085

So as per this definition of the breakeven point, at 18085 the put option should

neither make any money nor lose any money. To validate this let us apply the P&L

formula –

= Max (0, 18400 – 18085) – 315

= Max (0, 315) – 315

= 315 – 315

The result obtained in clearly in line with the expectation of the breakeven point.

Important note – The calculation of the intrinsic value, P&L, and Breakeven point

are all with respect to the expiry. So far in this module, we have assumed that you

as an option buyer or seller would set up the option trade with an intention to hold

the same till expiry.

But soon you will realize that that more often than not, you will initiate an options

trade only to close it much earlier than expiry. Under such a situation the

calculations of breakeven point may not matter much, however the calculation of

the P&L and intrinsic value does matter and there is a different formula to do the

same.

To put this more clearly let me assume two situations on the Bank Nifty Trade, we

know the trade has been initiated on 7

April 2015 and the expiry is on 30

April

2015–

1. What would be the P&L assuming spot is at 17000 on 30

April 2015?

2. What would be the P&L assuming spot is at 17000 on 15

April 2015 (or for that

matter any other date apart from the expiry date)

Answer to the first question is fairly simple, we can straight way apply the P&L

formula –

= Max (0, 18400 – 17000) – 315

= Max (0, 1400) – 315

= 1400 – 315

= 1085

Going on to the 2

question, if the spot is at 17000 on any other date apart from the

expiry date, the P&L is not going to be 1085, it will be higher. We will discuss why

this will be higher at an appropriate stage, but for now just keep this point in the

back of your mind.

5.5 – Put option buyer’s P&L payoff

If we connect the P&L points of the Put Option and develop a line chart, we should

be able to observe the generalizations we have made on the Put option buyers P&L.

Please find below the same –

Here are a few things that you should appreciate from the chart above, remember

18400 is the strike price –

1. The Put option buyer experienced a loss only when the spot price goes above the

strike price (18400 and above)

2. However this loss is limited to the extent of the premium paid

3. The Put Option buyer will experience an exponential gain as and when the spot

price trades below the strike price

4. The gains can be potentially unlimited

5. At the breakeven point (18085) the put option buyer neither makes money nor

losses money. You can observe that at the breakeven point, the P&L graph just

recovers from a loss making situation to a neutral situation. It is only above this

point the put option buyer would start to make money.

Key takeaways from this chapter

1. Buy a Put Option when you are bearish about the prospects of the underlying. In

other words a Put option buyer is profitable only when the underlying declines in

value

2. The intrinsic value calculation of a Put option is slightly different when compared to

the intrinsic value calculation of a call option

3. IV (Put Option) = Strike Price – Spot Price

4. The P&L of a Put Option buyer can be calculated as P&L = [Max (0, Strike Price –

Spot Price)] – Premium Paid

5. The breakeven point for the put option buyer is calculated as Strike – Premium

Paid

Module 5 — Options Theory for Professional Trading

Chapter 6

The Put Option selling

149

6.1 – Building the case

Previously we understood that, an option seller and the buyer are like two sides of

the same coin. They have a diametrically opposite view on markets. Going by this, if

the Put option buyer is bearish about the market, then clearly the put option seller

must have a bullish view on the markets. Recollect we looked at the Bank Nifty’s

chart in the previous chapter; we will review the same chart again, but from the

perspective of a put option seller.

The typical thought process for the Put Option Seller would be something like this –

1. Bank Nifty is trading at 18417

2. 2 days ago Bank Nifty tested its resistance level at 18550 (resistance level is

highlighted by a green horizontal line)

3. 18550 is considered as resistance as there is a price action zone at this level which is

well spaced in time (for people who are not familiar with the concept of resistance I

would suggest you read about it here)

4. I have highlighted the price action zone in a blue rectangular boxes

5. Bank Nifty has attempted to crack the resistance level for the last 3 consecutive

times

6. All it needs is 1 good push (maybe a large sized bank announcing decent results –

HDFC, ICICI, and SBI are expected to declare results soon)

7. A positive cue plus a move above the resistance will set Bank Nifty on the upward

trajectory

8. Hence writing the Put Option and collecting the premiums may sound like a good

idea

You may have a question at this stage – If the outlook is bullish, why write (sell) a put

option and why not just buy a call option?

Well, the decision to either buy a call option or sell a put option really depends on

how attractive the premiums are. At the time of taking the decision, if the call option

has a low premium then buying a call option makes sense, likewise if the put option

is trading at a very high premium then selling the put option (and therefore

collecting the premium) makes sense. Of course to figure out what exactly to do

(buying a call option or selling a put option) depends on the attractiveness of the

premium, and to judge how attractive the premium is you need some background

knowledge on ‘option pricing’. Of course, going forward in this module we will

understand option pricing.

So, with these thoughts assume the trader decides to write (sell) the 18400 Put

option and collect Rs.315 as the premium. As usual let us observe the P&L behavior

for a Put Option seller and make a few generalizations.

Do Note – when you write options (regardless of Calls or Puts) margins are blocked

in your account. We have discussed this perspective here, request you to go

through the same.

6.2 – P&L behavior for the put option seller

Please do remember the calculation of the intrinsic value of the option remains the

same for both writing a put option as well as buying a put option. However the P&L

calculation changes, which we will discuss shortly. We will assume various possible

scenarios on the expiry date and figure out how the P&L behaves.

Serial No.

Possible values of spot

Premium Received

Intrinsic Value (IV)

P&L (Premium – IV)

16195

+ 315

18400 – 16195 = 2205

315 – 2205 = – 1890

16510

+ 315

18400 – 16510 = 1890

315 – 1890 = – 1575

16825

+ 315

18400 – 16825 = 1575

315 – 1575 = – 1260

17140

+ 315

18400 – 17140 = 1260

315 – 1260 = – 945

17455

+ 315

18400 – 17455 = 945

315 – 945 = – 630

17770

+ 315

18400 – 17770 = 630

315 – 630 = – 315

18085

+ 315

18400 – 18085 = 315

315 – 315 = 0

18400

+ 315

18400 – 18400 = 0

315 – 0 = + 315

18715

+ 315

18400 – 18715 = 0

315 – 0 = + 315

19030

+ 315

18400 – 19030 = 0

315 – 0 = + 315

19345

+ 315

18400 – 19345 = 0

315 – 0 = + 315

19660

+ 315

18400 – 19660 = 0

315 – 0 = + 315

I would assume by now you will be in a position to easily generalize the P&L

behavior upon expiry, especially considering the fact that we have done the same

for the last 3 chapters. The generalizations are as below (make sure you set your

eyes on row 8 as it’s the strike price for this trade) –

1. The objective behind selling a put option is to collect the premiums and benefit

from the bullish outlook on market. Therefore as we can see, the profit stays flat at

Rs.315 (premium collected) as long as the spot price stays above the strike price.

1. Generalization 1 – Sellers of the Put Options are profitable as long as long as the

spot price remains at or higher than the strike price. In other words sell a put option

only when you are bullish about the underlying or when you believe that the

underlying will no longer continue to fall.

2. As the spot price goes below the strike price (18400) the position starts to make a

loss. Clearly there is no cap on how much loss the seller can experience here and it

can be theoretically be unlimited

1. Generalization 2 – A put option seller can potentially experience an unlimited loss

as and when the spot price goes lower than the strike price.

Here is a general formula using which you can calculate the P&L from writing a Put

Option position. Do bear in mind this formula is applicable on positions held till

expiry.

P&L = Premium Recieved – [Max (0, Strike Price – Spot Price)]

Let us pick 2 random values and evaluate if the formula works –

o 16510

o 19660

@16510 (spot below strike, position has to be loss making)

= 315 – Max (0, 18400 -16510)

= 315 – 1890

= – 1575

@19660 (spot above strike, position has to be profitable, restricted to premium

paid)

= 315 – Max (0, 18400 – 19660)

= 315 – Max (0, -1260)

= 315

Clearly both the results match the expected outcome.

Further, the breakdown point for a Put Option seller can be defined as a point

where the Put Option seller starts making a loss after giving away all the premium

he has collected –

Breakdown point = Strike Price – Premium Received

For the Bank Nifty, the breakdown point would be

= 18400 – 315

= 18085

So as per this definition of the breakdown point, at 18085 the put option seller

should neither make any money nor lose any money. Do note this also means at

this stage, he would lose the entire Premium he has collected. To validate this, let us

apply the P&L formula and calculate the P&L at the breakdown point –

= 315 – Max (0, 18400 – 18085)

= 315 – Max (0, 315)

= 315 – 315

The result obtained in clearly in line with the expectation of the breakdown point.

6.3 – Put option seller’s Payoff

If we connect the P&L points (as seen in the table earlier) and develop a line chart,

we should be able to observe the generalizations we have made on the Put option

seller’s P&L. Please find below the same –

Here are a few things that you should appreciate from the chart above, remember

18400 is the strike price –

1. The Put option seller experiences a loss only when the spot price goes below the

strike price (18400 and lower)

2. The loss is theoretically unlimited (therefore the risk)

3. The Put Option seller will experience a profit (to the extent of premium received) as

and when the spot price trades above the strike price

4. The gains are restricted to the extent of premium received

5. At the breakdown point (18085) the put option seller neither makes money nor

losses money. However at this stage he gives up the entire premium he has

received.

6. You can observe that at the breakdown point, the P&L graph just starts to buckle

down – from a positive territory to the neutral (no profit no loss) situation. It is only

below this point the put option seller starts to lose money.

And with these points, hopefully you should have got the essence of Put Option

selling. Over the last few chapters we have looked at both the call option and the

put option from both the buyer and sellers perspective. In the next chapter we will

quickly summarize the same and shift gear towards other essential concepts of

Options.

Key takeaways from this chapter

1. You sell a Put option when you are bullish on a stock or when you believe the stock

price will no longer go down

2. When you are bullish on the underlying you can either buy the call option or sell a

put option. The decision depends on how attractive the premium is

3. Option Premium pricing along with Option Greeks gives a sense of how attractive

the premiums are

4. The put option buyer and the seller have a symmetrically opposite P&L behavior

5. When you sell a put option you receive premium

6. Selling a put option requires you to deposit margin

7. When you sell a put option your profit is limited to the extent of the premium you

receive and your loss can potentially be unlimited

8. P&L = Premium received – Max [0, (Strike Price – Spot Price)]

9. Breakdown point = Strike Price – Premium Paid

Module 5 — Options Theory for Professional Trading

Chapter 7

Summarizing Call & Put Options

131

7.1 – Remember these graphs

Over the last few chapters we have looked at two basic option type’s i.e. the ‘Call

Option’ and the ‘Put Option’. Further we looked at four different variants originating

from these 2 options –

1. Buying a Call Option

2. Selling a Call Option

3. Buying a Put Option

4. Selling a Put Option

With these 4 variants, a trader can create numerous different combinations and

venture into some really efficient strategies generally referred to as ‘Option

Strategies’. Think of it this way – if you give a good artist a color palette and canvas

he can create some really interesting paintings, similarly a good trader can use

these four option variants to create some really good trades. Imagination and

intellect is the only requirement for creating these option trades. Hence before we

get deeper into options, it is important to have a strong foundation on these four

variants of options. For this reason, we will quickly summarize what we have learnt

so far in this module.

Please find below the pay off diagrams for the four different option variants –

Arranging the Payoff diagrams in the above fashion helps us understand a few

things better. Let me list them for you –

1. Let us start from the left side – if you notice we have stacked the pay off diagram of

Call Option (buy) and Call option (sell) one below the other. If you look at the payoff

diagram carefully, they both look like a mirror image. The mirror image of the payoff

emphasis the fact that the risk-reward characteristics of an option buyer and seller

are opposite. The maximum loss of the call option buyer is the maximum profit of

the call option seller. Likewise the call option buyer has unlimited profit potential,

mirroring this the call option seller has maximum loss potential

2. We have placed the payoff of Call Option (buy) and Put Option (sell) next to each

other. This is to emphasize that both these option variants make money only when

the market is expected to go higher. In other words, do not buy a call option or do

not sell a put option when you sense there is a chance for the markets to go down.

You will not make money doing so, or in other words you will certainly lose money

in such circumstances. Of course there is an angle of volatility here which we have

not discussed yet; we will discuss the same going forward. The reason why I’m

talking about volatility is because volatility has an impact on option premiums

3. Finally on the right, the pay off diagram of Put Option (sell) and the Put Option (buy)

are stacked one below the other. Clearly the pay off diagrams looks like the mirror

image of one another. The mirror image of the payoff emphasizes the fact that the

maximum loss of the put option buyer is the maximum profit of the put option

seller. Likewise the put option buyer has unlimited profit potential, mirroring this

the put option seller has maximum loss potential

Further, here is a table where the option positions are summarized.

Your Market View

Option Type

Position also called

Other Alternatives

Premium

Bullish

Call Option (Buy)

Long Call

Buy Futures or Buy Spot

Pay

Flat or Bullish

Put Option (Sell)

Short Put

Buy Futures or Buy Spot

Receive

Flat or Bearish

Call Option (Sell)

Short Call

Sell Futures

Receive

Bearish

Put Option (Buy)

Long Put

Sell Futures

Pay

It is important for you to remember that when you buy an option, it is also called a

‘Long’ position. Going by that, buying a call option and buying a put option is called

Long Call and Long Put position respectively.

Likewise whenever you sell an option it is called a ‘Short’ position. Going by that,

selling a call option and selling a put option is also called Short Call and Short Put

position respectively.

Now here is another important thing to note, you can buy an option under 2

circumstances –

1. You buy with an intention of creating a fresh option position

2. You buy with an intention to close an existing short position

The position is called ‘Long Option’ only if you are creating a fresh buy position. If

you are buying with and intention of closing an existing short position then it is

merely called a ‘square off’ position.

Similarly you can sell an option under 2 circumstances –

1. You sell with an intention of creating a fresh short position

2. You sell with an intention to close an existing long position

The position is called ‘Short Option’ only if you are creating a fresh sell (writing an

option) position. If you are selling with and intention of closing an existing long

position then it is merely called a ‘square off’ position.

7.2 – Option Buyer in a nutshell

By now I’m certain you would have a basic understanding of the call and put option

both from the buyer’s and seller’s perspective. However I think it is best to reiterate

a few key points before we make further progress in this module.

Buying an option (call or put) makes sense only when we expect the market to move

strongly in a certain direction. If fact, for the option buyer to be profitable the

market should move away from the selected strike price. Selecting the right strike

price to trade is a major task; we will learn this at a later stage. For now, here are a

few key points that you should remember –

1. P&L (Long call) upon expiry is calculated as P&L = Max [0, (Spot Price – Strike Price)] –

Premium Paid

2. P&L (Long Put) upon expiry is calculated as P&L = [Max (0, Strike Price – Spot Price)] –

Premium Paid

3. The above formula is applicable only when the trader intends to hold the long

option till expiry

4. The intrinsic value calculation we have looked at in the previous chapters is only

applicable on the expiry day. We CANNOT use the same formula during the series

5. The P&L calculation changes when the trader intends to square off the position well

before the expiry

6. The buyer of an option has limited risk, to the extent of premium paid. However he

enjoys an unlimited profit potential

7.2 – Option seller in a nutshell

The option sellers (call or put) are also called the option writers. The buyers and

sellers have exact opposite P&L experience. Selling an option makes sense when

you expect the market to remain flat or below the strike price (in case of calls) or

above strike price (in case of put option).

I want you to appreciate the fact that all else equal, markets are slightly favorable to

option sellers. This is because, for the option sellers to be profitable the market has

to be either flat or move in a certain direction (based on the type of option).

However for the option buyer to be profitable, the market has to move in a certain

direction. Clearly there are two favorable market conditions for the option seller

versus one favorable condition for the option buyer. But of course this in itself

should not be a reason to sell options.

Here are few key points you need to remember when it comes to selling options –

1. P&L for a short call option upon expiry is calculated as P&L = Premium Received – Max

[0, (Spot Price – Strike Price)]

2. P&L for a short put option upon expiry is calculated as P&L = Premium Received – Max

(0, Strike Price – Spot Price)

3. Of course the P&L formula is applicable only if the trader intends to hold the

position till expiry

4. When you write options, margins are blocked in your trading account

5. The seller of the option has unlimited risk but very limited profit potential (to the

extent of the premium received)

Perhaps this is the reason why Nassim Nicholas Taleb in his book “Fooled by

Randomness” says “Option writers eat like a chicken but shit like an elephant”. This

means to say that the option writers earn small and steady returns by selling

options, but when a disaster happens, they tend to lose a fortune.

Well, with this I hope you have developed a strong foundation on how a Call and Put

option behaves. Just to give you a heads up, the focus going forward in this module

will be on moneyness of an option, premiums, option pricing, option Greeks, and

strike selection. Once we understand these topics we will revisit the call and put

option all over again. When we do so, I’m certain you will see the calls and puts in a

new light and perhaps develop a vision to trade options professionally.

7.3 – A quick note on Premiums

Have a look at the snapshot below –

This is the snapshot of how the premium has behaved on an intraday basis

(30

April 2015) for BHEL. The strike under consideration is 230 and the option type

is a European Call Option (CE). This information is highlighted in the red box. Below

the red box, I have highlighted the price information of the premium. If you notice,

the premium of the 230 CE opened at Rs.2.25, shot up to make a high of Rs.8/- and

closed the day at Rs.4.05/-.

Think about it, the premium has gyrated over 350% intraday! i.e. from Rs.2.25/- to

Rs.8/-, and it roughly closed up 180% for the day i.e. from Rs.2.25/- to Rs.4.05/-.

Moves like this should not surprise you. These are fairly common to expect in the

options world.

Assume in this massive swing you managed to capture just 2 points while trading

this particular option intraday. This translates to a sweet Rs.2000/- in profits

considering the lot size is 1000 (highlighted in green arrow). In fact this is exactly

what happens in the real world. Traders just trade premiums. Hardly any traders

hold option contracts until expiry. Most of the traders are interested in initiating a

trade now and squaring it off in a short while (intraday or maybe for a few days) and

capturing the movements in the premium. They do not really wait for the options to

expire.

In fact you might be interested to know that a return of 100% or so while trading

options is not really a thing of surprise. But please don’t just get carried away with

what I just said; to enjoy such returns consistently you need develop a deep insight

into options.

Have a look at this snapshot –

This is the option contract of IDEA Cellular Limited, strike price is 190, expiry is on

April 2015 and the option type is a European Call Option . These details are

marked in the blue box. Below this we can notice the OHLC data, which quite

obviously is very interesting.

The 190CE premium opened the day at Rs.8.25/- and made a low of Rs.0.30/-. I will

skip the % calculation simply because it is a ridiculous figure for intraday. However

assume you were a seller of the 190 call option intraday and you managed to

capture just 2 points again, considering the lot size is 2000, the 2 point capture on

the premium translates to Rs.4000/- in profits intraday, good enough for that nice

dinner at Marriot with your better half J.

The point that I’m trying to make is that, traders (most of them) trade options only

to capture the variations in premium. They don’t really bother to hold till expiry.

However by no means I am suggesting that you need not hold until expiry, in fact I

do hold options till expiry in certain cases. Generally speaking option sellers tend to

hold contracts till expiry rather than option buyers. This is because if you have

written an option for Rs.8/- you will enjoy the full premium received i.e. Rs.8/- only

on expiry.

So having said that the traders prefer to trade just the premiums, you may have a

few fundamental questions cropping up in your mind. Why do premiums vary?

What is the basis for the change in premium? How can I predict the change in

premiums? Who decides what should be the premium price of a particular option?

Well, these questions and therefore the answers to these form the crux of option

trading. If you can master these aspects of an option, let me assure you that you

would set yourself on a professional path to trade options.

To give you a heads up – the answers to all these questions lies in understanding

the 4 forces that simultaneously exerts its influence on options premiums, as a

result of which the premiums vary. Think of this as a ship sailing in the sea. The

speed at which the ship sails (assume its equivalent to the option premium)

depends on various forces such as wind speed, sea water density, sea pressure, and

the power of the ship. Some forces tend to increase the speed of the ship, while

some tend to decrease the speed of the ship. The ship battles these forces and

finally arrives at an optimal sailing speed.

Likewise the premium of the option depends on certain forces called as the ‘Option

Greeks’. Crudely put, some Option Greeks tends to increase the premium, while

some try to reduce the premium. A formula called the ‘Black & Scholes Option

Pricing Formula’ employs these forces and translates the forces into a number,

which is the premium of the option.

Try and imagine this – the Option Greeks influence the option premium however

the Option Greeks itself are controlled by the markets. As the markets change on a

minute by minute basis, therefore the Option Greeks change and therefore the

option premiums!

Going forward in this module, we will understand each of these forces and its

characteristics. We will understand how the force gets influenced by the markets

and how the Option Greeks further influences the premium.

So the end objective here would be to be –

1. To get a sense of how the Option Greeks influence premiums

2. To figure out how the premiums are priced considering Option Greeks and their

influence

3. Finally keeping the Greeks and pricing in perspective, we need to smartly select

strike prices to trade

One of the key things we need to know before we attempt to learn the option

Greeks is to learn about the ‘Moneyness of an Option’. We will do the same in the

next chapter.

A quick note here – the topics going forward will get a little complex, although we

will try our best to simplify it. While we do that, we would request you to please be

thorough with all the concepts we have learnt so far.

Key takeaways from this chapter

1. Buy a call option or sell a put option only when you expect the market to go up

2. Buy a put option or sell a call option only when you expect the market to go down

3. The buyer of an option has an unlimited profit potential and limited risk (to the

extent of premium paid)

4. The seller of an option has an unlimited risk potential and limited reward (to the

extent of premium received)

5. Majority of option traders prefer to trade options only to capture the variation in

premiums

6. Option premiums tend to gyrate drastically – as an options trader you can expect

this to happen quite frequently

7. Premiums vary as a function of 4 forces called the Option Greeks

8. Black & Sholes option pricing formula employs four forces as inputs to give out a

price for the premium

9. Markets control the Option Greeks and the Greek’s variation itself

Module 5 — Options Theory for Professional Trading

Chapter 8

Moneyness of an Option Contract

161

8.1 – Intrinsic Value

The moneyness of an option contract is a classification method wherein each option

(strike) gets classified as either – In the money (ITM), At the money (ATM), or Out of

the money (OTM) option. This classification helps the trader to decide which strike

to trade, given a particular circumstance in the market. However before we get into

the details, I guess it makes sense to look through the concept of intrinsic value

again.

The intrinsic value of an option is the money the option buyer makes from an

options contract provided he has the right to exercise that option on the given day.

Intrinsic Value is always a positive value and can never go below 0. Consider this

example –

Underlying

CNX Nifty

Spot Value

8070

Option strike

8050

Option Type

Call Option (CE)

Days to expiry

Position

Long

Given this, assume you bought the 8050CE and instead of waiting for 15 days to

expiry you had the right to exercise the option today. Now my question to you is –

How much money would you stand to make provided you exercised the contract

today?

Do remember when you exercise a long option, the money you make is equivalent

to the intrinsic value of an option minus the premium paid. Hence to answer the

above question we need to calculate the intrinsic value of an option, for which we

need to pull up the call option intrinsic value formula from Chapter 3.

Here is the formula –

Intrinsic Value of a Call option = Spot Price – Strike Price

Let us plug in the values

= 8070 – 8050

= 20

So, if you were to exercise this option today, you are entitled to make 20 points

(ignoring the premium paid).

Here is a table which calculates the intrinsic value for various options strike (these

are just random values that I have used to drive across the concept) –

Option Type

Strike

Spot

Formula

Intrinsic Value

Remarks

Long Call

280

310

Spot Price – Strike Price

310 – 280 = 30

Long Put

1040

980

Strike Price – Spot Price

1040 -980 = 60

Long Call

920

918

Spot Price – Strike Price

918 – 920 = 0

Since IV cannot be -ve

Long Put

Strike Price – Spot Price

80 – 88 = 0

Since IV cannot be -ve

With this, I hope you are clear about the intrinsic value calculation for a given option

strike. Let me summarize a few important points –

1. Intrinsic value of an option is the amount of money you would make if you were to

exercise the option contract

2. Intrinsic value of an options contract can never be negative. It can be either zero or

a positive number

3. Call option Intrinsic value = Spot Price – Strike Price

4. Put option Intrinsic value = Strike Price – Spot price

Before we wrap up this discussion, here is a question for you – Why do you think the

intrinsic value cannot be a negative value?

To answer this, let us pick an example from the above table – Strike is 920, spot is

918, and option type is long call. Let us assume the premium for the 920 Call option

is Rs.15.

Now,

1. If you were to exercise this option, what do you get?

1. Clearly we get the intrinsic value.

2. How much is the intrinsic value?

1. Intrinsic Value = 918 – 920 = -2

3. The formula suggests we get ‘– Rs.2’. What does this mean?

1. This means Rs.2 is going from our pocket

4. Let us believe this is true for a moment, what will be the total loss?

1. 15 + 2 = Rs.17/-

5. But we know the maximum loss for a call option buyer is limited to the extent of

premium one pays, in this case it will be Rs.15/-

1. However if we include a negative intrinsic value this property of option payoff is not

obeyed (Rs.17/- loss as opposed to Rs.15/-). Hence in order to maintain the non

linear property of option payoff, the Intrinsic value can never be negative

6. You can apply the same logic to the put option intrinsic value calculation

Hopefully this should give you some insights into why the intrinsic value of an

option can never go negative.

8.2 – Moneyness of a Call option

With our discussions on the intrinsic value of an option, the concept of moneyness

should be quite easy to comprehend. Moneyness of an option is a classification

method which classifies each option strike based on how much money a trader is

likely to make if he were to exercise his option contract today. There are 3 broad

classifications –

1. In the Money (ITM)

2. At the Money (ATM)

3. Out of the Money (OTM)

And for all practical purposes I guess it is best to further classify these as –

1. Deep In the money

2. In the Money (ITM)

3. At the Money (ATM)

4. Out of the Money (OTM)

5. Deep Out of the Money

Understanding these option strike classification is very easy. All you need to do is

figure out the intrinsic value. If the intrinsic value is a non zero number, then the

option strike is considered ‘In the money’. If the intrinsic value is a zero the option

strike is called ‘Out of the money’. The strike which is closest to the Spot price is

called ‘At the money’.

Let us take up an example to understand this well. As of today (7

May 2015) the

value of Nifty is at 8060, keeping this in perspective I’ve take the snapshot of all the

available strike prices (the same is highlighted within a blue box). The objective is to

classify each of these strikes as ITM, ATM, or OTM. We will discuss the ‘Deep ITM’

and ‘Deep OTM’ later.

As you can notice from the image above, the available strike prices trade starts from

7100 all the way upto 8700.

We will first identify ‘At the Money Option (ATM)’ as this is the easiest to deal with.

From the definition of ATM option that we posted earlier we know, ATM option is

that option strike which is closest to the spot price. Considering the spot is at 8060,

the closest strike is probably 8050. If there was 8060 strike, then clearly 8060 would

be the ATM option. But in the absence of 8060 strike the next closest strike

becomes ATM. Hence we classify 8050 as, the ATM option.

Having established the ATM option (8050), we will proceed to identify ITM and OTM

options. In order to do this we will pick few strikes and calculate the intrinsic value.

1. 7100

2. 7500

3. 8050

4. 8100

5. 8300

Do remember the spot price is 8060, keeping this in perspective the intrinsic value

for the strikes above would be –

@ 7100

Intrinsic Value = 8060 – 7100

= 960

Non zero value, hence the strike should be In the Money (ITM) option

@7500

Intrinsic Value = 8060 – 7500

= 560

Non zero value, hence the strike should be In the Money (ITM) option

@8050

We know this is the ATM option as 8050 strike is closest to the spot price of 8060. So

we will not bother to calculate its intrinsic value.

@ 8100

Intrinsic Value = 8060 – 8100

= – 40

Negative intrinsic value, therefore the intrinsic value is 0. Since the intrinsic value is

0, the strike is Out of the Money (OTM).

@ 8300

Intrinsic Value = 8060 – 8300

= – 240

Negative intrinsic value, therefore the intrinsic value is 0. Since the intrinsic value is

0, the strike is Out of the Money (OTM).

You may have already sensed the generalizations (for call options) that exists here,

however allow me to restate the same again

1. All option strikes that are higher than the ATM strike are considered OTM

2. All option strikes that are below the ATM strike are considered ITM

In fact I would suggest you relook at the snapshot we just posted –

NSE presents ITM options with a pale yellow background and all OTM options have

a regular white background. Now let us look at 2 ITM options – 7500 and 8000. The

intrinsic value works out to be 560 and 60 respectively (considering the spot is at

8060). Higher the intrinsic value, deeper the moneyness of the option. Therefore

7500 strike is considered as ‘Deep In the Money’ option and 8000 as just ‘In the

money’ option.

I would encourage you to observe the premiums for all these strike prices

(highlighted in green box). Do you sense a pattern here? The premium decreases as

you traverse from ‘Deep ITM’ option to ‘Deep OTM option’. In other words ITM

options are always more expensive compared to OTM options.

8.3 – Moneyness of a Put option

Let us run through the same exercise to find out how strikes are classified as ITM

and OTM for Put options. Here is the snapshot of various strikes available for a Put

option. The strike prices on the left are highlighted in a blue box. Do note at the

time of taking the snap shot (8

May 2015) Nifty’s spot value is 8202.

As you can see there are many strike prices available right from 7100 to 8700. We

will first classify the ATM option and then proceed to identify ITM and OTM option.

Since the spot is at 8202, the nearest strike to spot should be the ATM option. As we

can see from the snapshot above there is a strike at 8200 which is trading at

Rs.131.35/-. This obviously becomes the ATM option.

We will now pick a few strikes above and below the ATM and figure out ITM and

OTM options. Let us go with the following strikes and evaluate their respective

intrinsic value (also called the moneyness) –

1. 7500

2. 8000

3. 8200

4. 8300

5. 8500

@ 7500

We know the intrinsic value of put option can be calculated as = Strike – Spot

Intrinsic Value = 7500 – 8200

= – 700

Negative intrinsic value, therefore the option is OTM

@ 8000

Intrinsic Value = 8000 – 8200

= – 200

Negative intrinsic value, therefore the option is OTM

@8200

8200 is already classified as ATM option, hence we will skip this and move ahead.

@ 8300

Intrinsic Value = 8300 – 8200

= +100

Positive intrinsic value, therefore the option is ITM

@ 8500

Intrinsic Value = 8500 – 8200

= +300

Positive intrinsic value, therefore the option is ITM

Hence, an easy generalization for Put options are –

1. All strikes higher than ATM options are considered ITM

2. All strikes lower than ATM options are considered OTM

And as you can see from the snapshot, the premiums for ITM options are much

higher than the premiums for the OTM options.

I hope you have got a clear understanding of how option strikes are classified based

on their moneyness. However you may still be wondering about the need to classify

options based on their moneyness. Well the answer to this lies in ‘Option Greeks’

again. As you briefly know by now, Option Greeks are the market forces which act

upon options strikes and therefore affect the premium associated with these

strikes. So a certain market force will have a certain effect on ITM option while at the

same time it will have a different effect on an OTM option. Hence classifying the

option strikes will help us in understanding the Option Greeks and their impact on

the premiums better.

8.4 – The Option Chain

The Option chain is a common feature on most of the exchanges and trading

platforms. The option chain is a ready reckoner of sorts that helps you identify all

the strikes that are available for a particular underlying and also classifies the strikes

based on their moneyness. Besides, the option chain also provides information such

as the premium price (LTP), bid –ask price, volumes, open interest etc for each of

the option strikes.

Have a look at the option chain of Ashoka Leyland Limited as published on NSE –

Few observations to help you understand the option chain better –

1. The underlying spot value is at Rs.68.7/- (highlighted in blue)

2. The Call options are on to the left side of the option chain

3. The Put options are on to the right side of the option chain

4. The strikes are stacked on an increasing order in the center of the option chain

5. Considering the spot at Rs.68.7, the closest strike is 67.5, hence that would be an

ATM option (highlighted in yellow)

6. For Call options – all option strikes lower than ATM options are ITM option, hence

they have a pale yellow background

7. For Call options – all option strikes higher than ATM options are OTM options, hence

they have a white background

8. For Put Options – all option strikes higher than ATM are ITM options, hence they

have a pale yellow background

9. For Put Options – all option strikes lower than ATM are OTM options, hence they

have a white background

10. The pale yellow and white background from NSE is just a segregation method to

bifurcate the ITM and OTM options. The color scheme is not a standard convention.

Here is the link to check the option chain for Nifty Options.

8.4 – The way forward

Having understood the basics of the call and put options both from the buyers and

sellers perspective and also having understood the concept of ITM, OTM, and ATM I

suppose we are all set to dwell deeper into options.

The next couple of chapters will be dedicated to understand Option Greeks and the

kind of impact they have on option premiums. Based on the Option Greeks impact

on the premiums, we will figure out a way to select the best possible strike to trade

for a given circumstance in the market. Further we will also understand how

options are priced by briefly running through the ‘Black & Scholes Option Pricing

Formula’. The ‘Black & Scholes Option Pricing Formula’ will help us understand

things like – Why Nifty 8200 PE is trading at 131 and not 152 or 102!

I hope you are as excited to learn about all these topics as we are to write about the

same. So please stay tuned.

Onwards to Option Greeks now!

Key takeaways from this chapter

1. The intrinsic value of an option is equivalent to the value of money the option buyer

makes provided if he were to exercise the contract

2. Intrinsic Value of an option cannot be negative, it is a non zero positive value

3. Intrinsic value of call option = Spot Price – Strike Price

4. Intrinsic value of put option = Strike Price – Spot Price

5. Any option that has an intrinsic value is classified as ‘In the Money’ (ITM) option

6. Any option that does not have an intrinsic value is classified as ‘Out of the Money’

(OTM) option

7. If the strike price is almost equal to spot price then the option is considered as ‘At

the money’ (ATM) option

8. All strikes lower than ATM are ITM options (for call options)

9. All strikes higher than ATM are OTM options (for call options)

10. All strikes higher than ATM are ITM options (for Put options)

11. All strikes lower than ATM are OTM options (for Put options)

12. When the intrinsic value is very high, it is called ‘Deep ITM’ option

13. Likewise when the intrinsic value is the least, it is called ‘Deep OTM’ option

14. The premiums for ITM options are always higher than the premiums for OTM option

15. The Option chain is a quick visualization to understand which option strike is ITM,

OTM, ATM (for both calls and puts) along with other information relevant to options.

Module 5 — Options Theory for Professional Trading

Chapter 9

The Option Greeks (Delta) Part 1

161

9.1 – Overview

Yesterday I watched the latest bollywood flick ‘Piku’. Quite nice I must say. After

watching the movie I was casually pondering over what really made me like Piku –

was it the overall storyline, or Amitabh Bachchan’s brilliant acting, or Deepika

Padukone’s charming screen presence, or Shoojit Sircar’s brilliant direction? Well, I

suppose it was a mix of all these factors that made the movie enjoyable.

This also made me realize, there is a remarkable similarity between a bollywood

movie and an options trade. Similar to a bollywood movie, for an options trade to

be successful in the market there are several forces which need to work in the

option trader’s favor. These forces are collectively called ‘The Option Greeks’. These

forces influence an option contract in real time, affecting the premium to either

increase or decrease on a minute by minute basis. To make matters complicated,

these forces not only influence the premiums directly but also influence each

another.

To put this in perspective think about these two bollywood actors – Aamir Khan and

Salman Khan. Movie buffs would recognize them as two independent acting forces

(similar to option Greeks) of Bollywood. They can independently influence the

outcome of the movie they act in (think of the movie as an options premium).

However if you put both these guys in a single flick, chances are that they will try to

pull one another down while at the same time push themselves up and at the same

time try to make the movie a success. Do you see the juggling around here? This

may not be a perfect analogy, but I hope it gives you a sense of what I’m trying to

convey.

Options Premiums, options Greeks, and the natural demand supply situation of the

markets influence each other. Though all these factors work as independent agents,

yet they are all intervened with one another. The final outcome of this mixture can

be assessed in the option’s premium. For an options trader, assessing the variation

in premium is most important. He needs to develop a sense for how these factors

play out before setting up an option trade.

So without much ado, let me introduce the Greeks to you –

1. Delta – Measures the rate of change of options premium based on the directional

movement of the underlying

2. Gamma – Rate of change of delta itself

3. Vega – Rate of change of premium based on change in volatility

4. Theta – Measures the impact on premium based on time left for expiry

We will discuss these Greeks over the next few chapters. The focus of this chapter is

to understand the Delta.

9.2 – Delta of an Option

Notice the following two snapshots here – they belong to Nifty’s 8250 CE option. The

first snapshot was taken at 09:18 AM when Nifty spot was at 8292.

A little while later…

Now notice the change in premium – at 09:18 AM when Nifty was at 8292 the call

option was trading at 144, however at 10:00 AM Nifty moved to 8315 and the same

call option was trading at 150.

In fact here is another snapshot at 10:55 AM – Nifty declined to 8288 and so did

the option premium (declined to 133).

From the above observations one thing stands out very clear – as and when the

value of the spot changes, so does the option premium. More precisely as we

already know – the call option premium increases with the increase in the spot

value and vice versa.

Keeping this in perspective, imagine this – you have predicted that Nifty will reach

8355 by 3:00 PM today. From the snapshots above we know that the premium will

certainly change – but by how much? What is the likely value of the 8250 CE

premium if Nifty reaches 8355?

Well, this is exactly where the ‘Delta of an Option’ comes handy. The Delta measures

how an options value changes with respect to the change in the underlying. In

simpler terms, the Delta of an option helps us answer questions of this sort – “By

how many points will the option premium change for every 1 point change in the

underlying?”

Therefore the Option Greek’s ‘Delta’ captures the effect of the directional movement

of the market on the Option’s premium.

The delta is a number which varies –

1. Between 0 and 1 for a call option, some traders prefer to use the 0 to 100 scale. So

the delta value of 0.55 on 0 to 1 scale is equivalent to 55 on the 0 to 100 scale.

2. Between -1 and 0 (-100 to 0) for a put option. So the delta value of -0.4 on the -1 to 0

scale is equivalent to -40 on the -100 to 0 scale

3. We will soon understand why the put option’s delta has a negative value associated

with it

At this stage I want to give you an orientation of how this chapter will shape up,

please do keep this at the back of your mind as I believe it will help you join the dots

better –

1. We will understand how we can use the Delta value for Call Options

2. A quick note on how the Delta values are arrived at

3. Understand how we can use the Delta value for Put Options

4. Delta Characteristics – Delta vs. Spot, Delta Acceleration (continued in next chapter)

5. Option positions in terms of Delta (continued in next chapter)

So let’s hit the road!

9.3 – Delta for a Call Option

We know the delta is a number that ranges between 0 and 1. Assume a call option

has a delta of 0.3 or 30 – what does this mean?

Well, as we know the delta measures the rate of change of premium for every unit

change in the underlying. So a delta of 0.3 indicates that for every 1 point change in

the underlying, the premium is likely change by 0.3 units, or for every 100 point

change in the underlying the premium is likely to change by 30 points.

The following example should help you understand this better –

Nifty @ 10:55 AM is at 8288

Option Strike = 8250 Call Option

Premium = 133

Delta of the option = + 0.55

Nifty @ 3:15 PM is expected to reach 8310

What is the likely option premium value at 3:15 PM?

Well, this is fairly easy to calculate. We know the Delta of the option is 0.55, which

means for every 1 point change in the underlying the premium is expected to

change by 0.55 points.

We are expecting the underlying to change by 22 points (8310 – 8288), hence the

premium is supposed to increase by

= 22*0.55

= 12.1

Therefore the new option premium is expected to trade around 145.1 (133+12.1)

Which is the sum of old premium + expected change in premium

Let us pick another case – what if one anticipates a drop in Nifty? What will happen

to the premium? Let us figure that out –

Nifty @ 10:55 AM is at 8288

Option Strike = 8250 Call Option

Premium = 133

Delta of the option = 0.55

Nifty @ 3:15 PM is expected to reach 8200

What is the likely premium value at 3:15 PM?

We are expecting Nifty to decline by – 88 points (8200 – 8288), hence the change in

premium will be –

= – 88 * 0.55

= – 48.4

Therefore the premium is expected to trade around

= 133 – 48.4

= 84.6 (new premium value)

As you can see from the above two examples, the delta helps us evaluate the

premium value based on the directional move in the underlying. This is extremely

useful information to have while trading options. For example assume you expect a

massive 100 point up move on Nifty, and based on this expectation you decide to

buy an option. There are two Call options and you need to decide which one to buy.

Call Option 1 has a delta of 0.05

Call Option 2 has a delta of 0.2

Now the question is, which option will you buy?

Let us do some math to answer this –

Change in underlying = 100 points

Call option 1 Delta = 0.05

Change in premium for call option 1 = 100 * 0.05

= 5

Call option 2 Delta = 0.2

Change in premium for call option 2 = 100 * 0.2

= 20

As you can see the same 100 point move in the underlying has different effects on

different options. In this case clearly the trader would be better off buying Call

Option 2. This should give you a hint – the delta helps you select the right option

strike to trade. But of course there are more dimensions to this, which we will

explore soon.

At this stage let me post a very important question – Why is the delta value for a call

option bound by 0 and 1? Why can’t the call option’s delta go beyond 0 and 1?

To help understand this, let us look at 2 scenarios wherein I will purposely keep the

delta value above 1 and below 0.

Scenario 1: Delta greater than 1 for a call option

Nifty @ 10:55 AM at 8268

Option Strike = 8250 Call Option

Premium = 133

Delta of the option = 1.5 (purposely keeping it above 1)

Nifty @ 3:15 PM is expected to reach 8310

What is the likely premium value at 3:15 PM?

Change in Nifty = 42 points

Therefore the change in premium (considering the delta is 1.5)

= 1.5*42

= 63

Do you notice that? The answer suggests that for a 42 point change in the

underlying, the value of premium is increasing by 63 points! In other words, the

option is gaining more value than the underlying itself. Remember the option is a

derivative contract, it derives its value from its respective underlying, hence it can

never move faster than the underlying.

If the delta is 1 (which is the maximum delta value) it signifies that the option is

moving in line with the underlying which is acceptable, but a value higher than 1

does not make sense. For this reason the delta of an option is fixed to a maximum

value of 1 or 100.

Let us extend the same logic to figure out why the delta of a call option is lower

bound to 0.

Scenario 2: Delta lesser than 0 for a call option

Nifty @ 10:55 AM at 8288

Option Strike = 8300 Call Option

Premium = 9

Delta of the option = – 0.2 (have purposely changed the value to below 0, hence

negative delta)

Nifty @ 3:15 PM is expected to reach 8200

What is the likely premium value at 3:15 PM?

Change in Nifty = 88 points (8288 -8200)

Therefore the change in premium (considering the delta is -0.2)

= -0.2*88

= -17.6

For a moment we will assume this is true, therefore new premium will be

= -17.6 + 9

= – 8.6

As you can see in this case, when the delta of a call option goes below 0, there is a

possibility for the premium to go below 0, which is impossible. At this point do

recollect the premium irrespective of a call or put can never be negative. Hence for

this reason, the delta of a call option is lower bound to zero.

9.4 – Who decides the value of the Delta?

The value of the delta is one of the many outputs from the Black & Scholes option

pricing formula. As I have mentioned earlier in this module, the B&S formula takes

in a bunch of inputs and gives out a few key outputs. The output includes the

option’s delta value and other Greeks. After discussing all the Greeks, we will also go

through the B&S formula to strengthen our understanding on options. However for

now, you need to be aware that the delta and other Greeks are market driven

values and are computed by the B&S formula.

However here is a table which will help you identify the approximate delta value for

a given option –

Option Type

Approx Delta value (CE)

Approx Delta value (PE)

Deep ITM

Between + 0.8 to + 1

Between – 0.8 to – 1

Slightly ITM

Between + 0.6 to + 1

Between – 0.6 to – 1

ATM

Between + 0.45 to + 0.55

Between – 0.45 to – 0.55

Slightly OTM

Between + 0.45 to + 0.3

Between – 0.45 to -0.3

Deep OTM

Between + 0.3 to + 0

Between – 0.3 to – 0

Of course you can always find out the exact delta of an option by using a B&S option

pricing calculator.

9.5 – Delta for a Put Option

Do recollect the Delta of a Put Option ranges from -1 to 0. The negative sign is just

to illustrate the fact that when the underlying gains in value, the value of premium

goes down. Keeping this in mind, consider the following details –

Parameters

Values

Underlying

Nifty

Strike

8300

Spot value

8268

Premium

128

Delta

-0.55

Expected Nifty Value (Case 1)

8310

Expected Nifty Value (Case 2)

8230

Note – 8268 is a slightly ITM option, hence the delta is around -0.55 (as indicated

from the table above).

The objective is to evaluate the new premium value considering the delta value to

be -0.55. Do pay attention to the calculations made below.

Case 1: Nifty is expected to move to 8310

Expected change = 8310 – 8268

= 42

Delta = – 0.55

= -0.55*42

= -23.1

Current Premium = 128

New Premium = 128 -23.1

= 104.9

Here I’m subtracting the value of delta since I know that the value of a Put option

declines when the underlying value increases.

Case 2: Nifty is expected to move to 8230

Expected change = 8268 – 8230

= 38

Delta = – 0.55

= -0.55*38

= -20.9

Current Premium = 128

New Premium = 128 + 20.9

= 148.9

Here I’m adding the value of delta since I know that the value of a Put option gains

when the underlying value decreases.

I hope with the above two Illustrations you are now clear on how to use the Put

Option’s delta value to evaluate the new premium value. Also, I will take the liberty

to skip explaining why the Put Option’s delta is bound between -1 and 0.

In fact I would encourage the readers to apply the same logic we used while

understanding why the call option’s delta is bound between 0 and 1, to understand

why Put option’s delta is bound between -1 and 0.

In the next chapter we will dig deeper into Delta and understand some of its

characteristics.

Key takeaways from this chapter

1. Option Greeks are forces that influence the premium of an option

2. Delta is an Option Greek that captures the effect of the direction of the market

3. Call option delta varies between 0 and 1, some traders prefer to use 0 to 100.

4. Put option delta varies between -1 and 0 (-100 to 0)

5. The negative delta value for a Put Option indicates that the option premium and

underlying value moves in the opposite direction

6. ATM options have a delta of 0.5

7. ITM option have a delta of close to 1

8. OTM options have a delta of close to 0.

Module 5 — Options Theory for Professional Trading

Chapter 10

Delta (Part 2)

146

10.1 – Model Thinking

The previous chapter gave you a sneak peek into the first option Greek – the Delta.

Besides discussing the delta, there was another hidden agenda in the previous

chapter – to set you on a ‘model thinking’ path. Let me explain what I mean by this –

the previous chapter opened up a new window to evaluate options. The window

threw open different option trading perspectives – hopefully you now no longer

think about options in a one-dimensional perspective.

For instance going forward if you have view on markets (bullish for example)

you may not strategize your trade this way – ‘My view is bullish, therefore it makes

sense to either buy a call option or collect premium by selling a put option’.

Rather you may strategize this way – “My view is bullish as I expect the market to

move by 40 points, therefore it makes sense to buy an option which has a delta of

0.5 or more as the option is expected to gain at least 20 points for the given 40 point

move in the market”.

See the difference between the two thought processes? While the former is a bit

naïve and casual, the latter is well defined and quantitative in nature. The

expectation of a 20 point move in the option premium was an outcome of a formula

that we explored in the previous chapter –

Expected change in option premium = Option Delta * Points change in

underlying

The above formula is just one piece in the whole game plan. As and when we

discover the other Greeks, the evaluation metric becomes more quantitative and in

the process the trade selection becomes more scientifically streamlined. Point is –

the thinking going forward will be guided by equations and numbers and ‘casual

trading thoughts’ will have very little scope. I know there are many traders who

trade just with a few random thoughts and some may even be successful. However

this is not everybody’s cup of tea. The odds are better when you put numbers in

perspective – and this happens when you develop ‘model thinking’.

So please do keep model thinking framework in perspective while analyzing options,

as this will help you setup systematic trades.

10.2 – Delta versus spot price

In the previous chapter we looked at the significance of Delta and also understood

how one can use delta to evaluate the expected change in premium. Before we

proceed any further, here is a quick recap from the previous chapter –

1. Call options has a +ve delta. A Call option with a delta of 0.4 indicates that for every

1 point gain/loss in the underlying the call option premium gains/losses 0.4 points

2. Put options has a –ve delta. A Put option with a delta of -0.4 Indicates that for every

1 point loss/gain in the underlying the put option premium gains/losses 0.4 points

3. OTM options have a delta value between 0 and 0.5, ATM option has a delta of 0.5,

and ITM option has a delta between 0.5 and 1.

Let me take cues from the 3

point here and make some deductions. Assume Nifty

Spot is at 8312, strike under consideration is 8400, and option type is CE (Call

option, European).

1. What is the approximate Delta value for the 8400 CE when the spot is 8312?

1. Delta should be between 0 and 0.5 as 8400 CE is OTM. Let us assume Delta is 0.4

2. Assume Nifty spot moves from 8312 to 8400, what do you think is the Delta value?

1. Delta should be around 0.5 as the 8400 CE is now an ATM option

3. Further assume Nifty spot moves from 8400 to 8500, what do you think is the Delta

value?

1. Delta should be closer to 1 as the 8400 CE is now an ITM option. Let us say 0.8.

4. Finally assume Nifty Spot cracks heavily and drops back to 8300 from 8500, what

happens to delta?

1. With the fall in spot, the option has again become an OTM from ITM, hence the

value of delta also falls from 0.8 to let us say 0.35.

5. What can you deduce from the above 4 points?

1. Clearly as and when the spot value changes, the moneyness of an option changes,

and therefore the delta also changes.

Now this is a very important point here – the delta changes with changes in the

value of spot. Hence delta is a variable and not really a fixed entity. Therefore if an

option has a delta of 0.4, the value is likely to change with the change in the value of

the underlying.

Have a look at the chart below – it captures the movement of delta versus the spot

price. The chart is a generic one and not specific to any particular option or strike as

such. As you can see there are two lines –

1. The blue line captures the behavior of the Call option’s delta (varies from 0 to 1)

2. The red line captures the behavior of the Put option’s delta (varies from -1 to 0)

Let us understand this better –

This is a very interesting chart, and to begin with I would suggest you look at only

the blue line and ignore the red line completely. The blue line represents the delta

of a call option. The graph above captures few interesting characteristics of the

delta; let me list them for you (meanwhile keep this point in the back of your mind –

as and when the spot price changes, the moneyness of the option also changes) –

1. Look at the X axis – starting from left the moneyness increases as the spot price

traverses from OTM to ATM to ITM

2. Look at the delta line (blue line) – as and when the spot price increases so does the

delta

3. Notice at OTM the delta is flattish near 0 – this also means irrespective of how much

the spot price falls ( going from OTM to deep OTM) the option’s delta will remain at

1. Remember the call option’s delta is lower bound by 0

4. When the spot moves from OTM to ATM the delta also starts to pick up (remember

the option’s moneyness also increases)

1. Notice how the delta of option lies within 0 to 0.5 range for options that are less

than ATM

5. At ATM, the delta hits a value of 0.5

6. When the spot moves along from the ATM towards ITM the delta starts to move

beyond the 0.5 mark

7. Notice the delta starts to fatten out when it hits a value of 1

1. This also implies that as and when the delta moves beyond ITM to say deep ITM the

delta value does not change. It stays at its maximum value of 1.

You can notice similar characteristics for the Put Option’s delta (red line).

10.3 – The Delta Acceleration

If you are fairly involved in the options world you may have heard of bizarre stories

of how traders double or triple their money by trading OTM option. If you have not

heard such stories, let me tell you one – It was 17

May 2009 (Sunday), the election

results were declared, the UPA Government got re-elected at the center and

Dr.Manmohan Singh came back as the country’s Prime Minister to serve his

term. Stock markets likes stability at the center and we all knew that the market

would rally the next day i.e. 18

May 2009. The previous day Nifty had closed at

3671.

Zerodha was not born then, we were just a bunch of traders trading our own capital

along with a few clients. One of our associates had taken a huge risk few days prior

to 17

May – he bought far off options (OTM) worth Rs.200,000/-. A dare devil act

this was considering the fact that nobody can really predict the outcome of a

general election. Obviously he would benefit if the market rallied, but for the market

to rally there were many factors at play. Along with him, we too were very anxious

to figure out what would happen. Finally the results were declared and we all knew

he would make money on 18

May – but none of us really knew to what extent he

would stand to benefit.

May 2009, a day that I cannot forget – markets opened at 9:55 AM (that was the

market opening time back then), it was a big bang open for market, Nifty

immediately hit an upper circuit and the markets froze. Within a matter of few

minutes Nifty rallied close to 20% to close the day at 4321! The exchanges decided

to close the market at 10:01 AM as it was overheated…and thus it was the shortest

working day of my life.

Here is the chart that highlights that day’s market move –

In the whole process our dear associate had made a sweet fortune. At 10:01 AM on

that glorious Monday morning, his option were valued at Rs.28,00,000/- a whopping

1300% gain all achieved overnight! This is the kind of trades that almost all traders

including me aspire to experience.

Anyway, let me ask you a few questions regarding this story and that will also bring

us back to the main topic –

1. Why do you think our associate choose to buy OTM options and not really ATM or

ITM options?

100

2. What would have happened if he had bought an ITM or ATM option instead?

Well the answers to these questions lies in this graph –

This graph talks about the ‘Delta Acceleration’ – there are 4 delta stages mentioned

in the graph, let us look into each one of them.

Before we move ahead with the following discussion some points for you here –

o I would advise you to pay a lot of attention to the following discussion, these are

some of the really important points to know and remember

o Do recollect and revise the delta table (option type, approximate delta value etc)

from the previous chapter

o Please do bear in mind the delta and premium numbers used here is an intelligent

assumption for the sake of this illustration –

Predevelopment – This is the stage when the option is OTM or deep OTM. The

delta here is close to 0. The delta will remain close to 0 even when the option moves

from deep OTM to OTM. For example when spot is 8400, 8700 Call Option is Deep

OTM, which is likely to have a delta of 0.05. Now even if the spot moves from 8400

to let us say 8500, the delta of 8700 Call option will not move much as 8700 CE is still

an OTM option. The delta will still be a small non – zero number.

101

So if the premium for 8700 CE when spot is at 8400 is Rs.12, then when Nifty moves

to 8500 (100 point move) the premium is likely to move by 100 * 0.05 = 5 points.

Hence the new premium will be Rs.12 + 5 = Rs.17/-. However the 8700 CE is now

considered slightly OTM and not really deep OTM.

Most important to note – the change in premium value in absolute terms maybe

small (Rs.5/-) but in percentage terms the Rs.12/- option has changed by 41.6% to

Rs.17/-

Conclusion – Deep OTM options tends to put on an impressive percentage however

for this to happen the spot has to move by a large value.

Recommendation – avoid buying deep OTM options because the deltas are really

small and the underlying has to move massively for the option to work in your favor.

There is more bang for the buck elsewhere. However for the very same reason

selling deep OTM makes sense, but we will evaluate when to sell these options

when we take up the Greek ‘Theta’.

Take off & Acceleration – This is the stage when the option transitions from OTM

to ATM. This is where the maximum bang for the buck lies, and therefore the risk.

Consider this – Nifty spot @ 8400, Strike is 8500 CE, option is slightly OTM, delta is

0.25, Premium is Rs.20/-.

Spot moves from 8400 to 8500 (100 point), to figure out what happens on the

premium side, let us do some math –

Change in underlying = 100

Delta for 8500 CE = 0.25

Premium change = 100 * 0.25 = 25

New premium = Rs.20 + 25 = Rs.45/-

Percentage change = 125%

Do you see that? For the same 100 point move slightly OTM options behaves very

differently.

Conclusion – The slightly OTM option which usually has a delta value of say 0.2 or

0.3 is more sensitive to changes in the underlying. For any meaningful change in the

underlying the percentage change in the slightly OTM options is very impressive. In

fact this is exactly how option traders double or triple their money i.e. by buying

slightly OTM options when they expect big moves in the underlying. But I would like

to remind you that this is just one face of the cube, there are other faces we still

need to explore.

102

Recommendation – Buying slightly OTM option is more expensive than buying

deep OTM options, but if you get your act right you stand to make a killing.

Whenever you buy options, consider buying slightly OTM options (of course

assuming there is plenty of time to expiry, we will talk about this later).

Let us take this forward and see how the ATM option would react for the same 100

point move.

Spot = 8400

Strike = 8400 (ATM)

Premium = Rs.60/-

Change in underlying = 100

Delta for 8400 CE = 0.5

Premium change = 100 * 0.5 = 50

New premium = Rs.60 + 50 = Rs.110/-

Percentage change = 83%

Conclusion – ATM options are more sensitive to changes in the spot when

compared to OTM options. Now because the ATM’s delta is high the underlying

need not really move by a large value. Even if the underlying moves by a small value

the option premium changes. However buying ATM options are more expensive

when compared to OTM options.

Recommendation – Buy ATM options when you want to play safe. The ATM option

will move even if the underlying does not move by a large value. Also as a corollary,

do not attempt to sell an ATM option unless you are very sure about what you are

doing.

Stabilization – When the option transitions from ATM to ITM and Deep ITM the

delta starts to stabilize at 1. As we can see from the graph, the delta starts to flatten

out when hits the value of 1. This means the option can be ITM or deep ITM but the

delta gets fixed to 1 and would not change in value.

Let us see how this works –

Nifty Spot = 8400

Option 1 = 8300 CE Strike, ITM option, Delta of 0.8, and Premium is Rs.105

Option 2 = 8200 CE Strike, Deep ITM Option, Delta of 1.0, and Premium is Rs.210

Change in underlying = 100 points, hence Nifty moves to 8500.

103

Given this let us see how the two options behave –

Change in premium for Option 1 = 100 * 0.8 = 80

New Premium for Option 1 = Rs.105 + 80 = Rs.185/-

Percentage Change = 80/105 = 76.19%

Change in premium for Option 2 = 100 * 1 = 100

New Premium for Option 2 = Rs.210 + 100 = Rs.310/-

Percentage Change = 100/210 = 47.6%

Conclusion – In terms of the absolute change in the number of points, the deep ITM

option scores over the slightly ITM option. However in terms of percentage change it

is the other way round. Clearly ITM options are more sensitive to the changes in the

underlying but certainly most expensive.

Most importantly notice the change in the deep ITM option (delta 1) for a change of

100 points in the underlying there is a change of 100 points in the option

premium. This means to say when you buy a deep ITM option it is as good as

buying the underlying itself. This is because whatever is the change in the

underlying, the deep ITM option will experience the same change.

Recommendation – Buy the ITM options when you want to play very safe. When I

say safe, I’m contrasting the deep ITM option with deep OTM option. The ITM

options have a high delta, which means they are most sensitive to changes in the

underlying.

Deep ITM option moves in line with the underlying, this means you can substitute a

deep ITM option to a futures contract!

Think about this –

Nifty Spot @ 8400

Nifty Futures = 8409

Strike = 8000 (deep ITM)

Premium = 450

Delta = 1.0

Change in spot = 30 points

New Spot value = 8430

104

Change in Futures = 8409 + 30 = 8439 à Reflects the entire 30 point change

Change Option Premium = 1*30 = 30

New Option Premium = 30 + 450 = 480 à Reflects the entire 30 point change

So the point is, both futures and Deep ITM options react very similar to the changes

in the underlying. Hence you are better off buying a Deep ITM option and therefore

lessen your margin burden. However if you opt to do this, you need to constantly

make sure that the Deep ITM option continues to remain Deep ITM (in other words

make sure the delta is always 1), plus do keep an eye on the liquidity of the contract.

I would suspect that at this stage the information contained in this chapter could be

an overdose, especially if you are exploring the Greeks for the first time. I would

suggest you take your time to learn this one bit at a time.

There are few more angles we need to explore with respect to the delta, but will do

that in the next chapter. However before we conclude this chapter let us summarize

the discussion with the help of a table.

This table will help us understand how different options behave differently given a

certain change in the underlying.

I’ve considered Bajaj Auto as the underlying. The price is 2210 and the expectation is

a 30 point change in the underlying (which means we are expecting Bajaj Auto to hit

2240). We will also assume there is plenty of time to expiry; hence time is not really

a concern.

Moneyness

Strike

Delta

Old Premium

Change in Premium

New Premium

% Change

Deep OTM

2400

0.05

Rs.3/-

30* 0.05 = 1.5

3+1.5 = 4.5

50%

Slightly OTM

2275

0.3

Rs.7/-

30*0.3 = 9

7 +9 = 16

129%

ATM

2210

0.5

Rs.12/-

30*0.5 = 15

12+15 = 27

125%

Slightly ITM

2200

0.7

Rs.22/-

30*0.7 = 21

22+21 = 43

95.45%

Deep ITM

2150

Rs.75/-

30*1 = 30

75 + 30 =105

40%

105

As you can see each option behaves differently for the same move in the

underlying.

Before I wrap this chapter – I narrated a story to you earlier in this chapter following

which I posted few questions. Perhaps you can now revisit the questions and you

will hopefully know the answers .

Key takeaways from this chapter

1. Model Thinking helps in developing a scientifically streamlined approach to trading

2. The Delta changes as and when the spot value changes

3. As the option transitions from OTM to ATM to ITM, so does the delta

4. Delta hits a value of 0.5 for ATM options

5. Delta predevelopment is when the option transitions from Deep OTM to OTM

6. Delta Take off and acceleration is when the option transitions from OTM to ATM

7. Delta stabilization is when the option transitions from ATM to ITM to Deep ITM

8. Buying options in the take off stage tends to give high % return

9. Buying Deep ITM option is as good as buying the underlying.

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Module 5 — Options Theory for Professional Trading

Chapter 11

Delta (Part 3)

118

11.1 – Add up the Deltas

Here is an interesting characteristic of the Delta – The Deltas can be added up!

Let me explain – we will go back to the Futures contract for a moment. We know for

every point change in the underlying’s spot value the futures also changes by 1

point. For example if Nifty Spot moves from 8340 to 8350 then the Nifty Futures will

also move from 8347 to 8357 (i.e. assuming Nifty Futures is trading at 8347 when

the spot is at 8340). If we were to assign a delta value to Futures, clearly the future’s

delta would be 1 as we know for every 1 point change in the underlying the futures

also changes by 1 point.

Now, assume I buy 1 ATM option which has a delta of 0.5, then we know that for

every 1 point move in the underlying the option moves by 0.5 points. In other words

owning 1 ATM option is as good as holding half futures contract. Given this, if I hold

2 such ATM contracts, then it as good as holding 1 futures contract because the

delta of the 2 ATM options i.e. 0.5 and 0.5, which adds up to total delta of 1! In other

words the deltas of two or more option contracts can be added to evaluate the total

delta of the position.

Let us take up a few case studies to understand this better –

Case 1 – Nifty spot at 8125, trader has 3 different Call option.

Sl No

Contract

Classification

Lots

Delta

Position Delta

107

8000 CE

ITM

1 -Buy

0.7

+ 1 * 0.7 = + 0.7

8120 CE

ATM

1 -Buy

0.5

+ 1 * 0.5 = + 0.5

8300 CE

Deep OTM

1- Buy

0.05

+ 1 * 0.05 = + 0.05

Total Delta of positions

= 0.7 + 0.5 + 0.05 = + 1.25

Observations –

1. The positive sign next to 1 (in the Position Delta column) indicates ‘Long’ position

2. The combined positions have a positive delta i.e. +1.25. This means both the

underlying and the combined position moves in the same direction

3. For every 1 point change in Nifty, the combined position changes by 1.25 points

4. If Nifty moves by 50 points, the combined position is expected to move by 50 * 1.25

= 62.5 points

Case 2 – Nifty spot at 8125, trader has a combination of both Call and Put

options.

Sl No

Contract

Classification

Lots

Delta

Position Delta

8000 CE

ITM

1- Buy

0.7

+ 1*0.7 =0.7

8300 PE

Deep ITM

1- Buy

– 1.0

+ 1*-1.0 = -1.0

8120 CE

ATM

1- Buy

0.5

+ 1*0.5 = 0.5

8300 CE

Deep OTM

1- Buy

0.05

+ 1*0.05 = 0.05

Total Delta of positions

0.7 – 1.0 + 0.5 + 0.05 = + 0.25

Observations –

108

1. The combined positions have a positive delta i.e. +0.25. This means both the

underlying and the combined position move in the same direction

2. With the addition of Deep ITM PE, the overall position delta has reduced, this means

the combined position is less sensitive to the directional movement of the market

3. For every 1 point change in Nifty, the combined position changes by 0.25 points

4. If Nifty moves by 50 points, the combined position is expected to move by 50 * 0.25

= 12.5 points

5. Important point to note here – Deltas of the call and puts can be added as long as it

belongs to the same underlying.

Case 3 – Nifty spot at 8125, trader has a combination of both Call and Put

options. He has 2 lots Put option here.

Sl No

Contract

Classification

Lots

Delta

Position Delta

8000 CE

ITM

1- Buy

0.7

+ 1 * 0.7 = + 0.7

8300 PE

Deep ITM

2- Buy

-1

+ 2 * (-1.0) = -2.0

8120 CE

ATM

1- Buy

0.5

+ 1 * 0.5 = + 0.5

8300 CE

Deep OTM

1- Buy

0.05

+ 1 * 0.05 = + 0.05

Total Delta of positions

0.7 – 2 + 0.5 + 0.05 = – 0.75

Observations –

1. The combined positions have a negative delta. This means the underlying and the

combined option position move in the opposite direction

2. With an addition of 2 Deep ITM PE, the overall position has turned delta negative,

this means the combined position is less sensitive to the directional movement of

the market

3. For every 1 point change in Nifty, the combined position changes by – 0.75 points

4. If Nifty moves by 50 points, the position is expected to move by 50 * (- 0.75) = -37.5

points

Case 4 – Nifty spot at 8125, the trader has Calls and Puts of the same strike,

same underlying.

109

Sl No

Contract

Classification

Lots

Delta

Position Delta

8100 CE

ATM

1- Buy

0.5

+ 1 * 0.5 = + 0.5

8100 PE

ATM

1- Buy

-0.5

+ 1 * (-0.5) = -0.5

Total Delta of positions

+ 0.5 – 0.5 = 0

Observations –

1. The 8100 CE (ATM) has a positive delta of + 0.5

2. The 8100 PE (ATM) has a negative delta of – 0.5

3. The combined position has a delta of 0, which implies that the combined position

does not get impacted by any change in the underlying

1. For example – If Nifty moves by 100 points, the change in the options positions will be 100 * 0 = 0

4. Positions such as this – which have a combined delta of 0 are also called ‘Delta

Neutral’ positions

5. Delta Neutral positions do not get impacted by any directional change. They behave

as if they are insulated to the market movements

6. However Delta neutral positions react to other variables like Volatility and Time. We

will discuss this at a later stage.

Case 5 – Nifty spot at 8125, trader has sold a Call Option

Sl No

Contract

Classification

Lots

Delta

Position Delta

8100 CE

ATM

1- Sell

0.5

– 1 * 0.5 = – 0.5

8100 PE

ATM

1- Buy

-0.5

+ 1 * (-0.5) = – 0.5

Total Delta of positions

– 0.5 – 0.5 = – 1.0

Observations –

1. The negative sign next to 1 (in the Position Delta column) indicates ‘short’ position

110

2. As we can see a short call option gives rise to a negative delta – this means the

option position and the underlying move in the opposite direction. This is quite

intuitive considering the fact that the increase in spot value results in a loss to the

call option seller

3. Likewise if you short a PUT option the delta turns positive

1. -1 * (-0.5) = +0.5

Lastly just consider a case wherein the trader has 5 lots long deep ITM option. We

know the total delta of such position would + 5 * + 1 = + 5. This means for every 1

point change in the underlying the combined position would change by 5 points in

the same direction.

Do note the same can be achieved by shorting 5 deep ITM PUT options –

– 5 * – 1 = + 5

-5 indicate 5 short positions and -1 is the delta of deep ITM Put options.

The above case study discussions should give you a perspective on how to add up

the deltas of the individual positions and figure out the overall delta of the

positions. This technique of adding up the deltas is very helpful when you have

multiple option positions running simultaneously and you want to identify the

overall directional impact on the positions.

In fact I would strongly recommend you always add the deltas of individual position

to get a perspective – this helps you understand the sensitivity and leverage of your

overall position.

Also, here is another important point you need to remember –

Delta of ATM option = 0.5

If you have 2 ATM options = delta of the position is 1

So, for every point change in the underlying the overall position also changes by 1

point (as the delta is 1). This means the option mimics the movement of a Futures

contract. However, do remember these two options should not be considered as a

surrogate for a futures contract. Remember the Futures contract is only affected by

the direction of the market, however the options contracts are affected by many

other variables besides the direction of the markets.

There could be times when you would want to substitute the options contract

instead of futures (mainly from the margins perspective) – but whenever you do so

be completely aware of its implications, more on this topic as we proceed.

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11.2 – Delta as a probability

Before we wrap up our discussion on Delta, here is another interesting application

of Delta. You can use the Delta to gauge the probability of the option contract to

expire in the money.

Let me explain – when a trader buys an option (irrespective of Calls or Puts), what is

that he aspires? For example what do you expect when you buy Nifty 8000 PE when

the spot is trading at 8100? (Note 8000 PE is an OTM option here). Clearly we expect

the market to fall so that the Put option starts to make money for us.

In fact the trader hopes the spot price falls below the strike price so that the option

transitions from an OTM option to ITM option – and in the process the premium

goes higher and the trader makes money.

The trader can use the delta of an option to figure out the probability of the option

to transition from OTM to ITM.

In the example 8000 PE is slightly OTM option; hence its delta must be below 0.5, let

us fix it to 0.3 for the sake of this discussion.

Now to figure out the probability of the option to transition from OTM to ITM,

simply convert the delta to a percentage number.

When converted to percentage terms, delta of 0.3 is 30%. Hence there is only 30%

chance for the 8000 PE to transition into an ITM option.

Interesting right? Now think about this situation – although an arbitrary situation,

this in fact is a very real life market situation –

1. 8400 CE is trading at Rs.4/-

2. Spot is trading at 8275

3. There are two day left for expiry – would you buy this option?

Well, a typical trader would think that this is a low cost trade, after all the premium

is just Rs.4/- hence there is nothing much to lose. In fact the trader could even

convince himself thinking that if the trade works in his favor, he stands a chance to

make a huge profit.

Fair enough, in fact this is how options work. But let’s put on our ‘Model Thinking’

hat and figure out if this makes sense –

1. 8400 CE is deep OTM call option considering spot is at 8275

2. The delta of this option could be around 0.1

3. Delta suggests that there is only 10% chance for the option to expire ITM

4. Add to this the fact that there are only 2 more days to expiry – the

case against buying this option becomes stronger!

112

A prudent trader would never buy this option. However don’t you think it makes

perfect sense to sell this option and pocket the premium? Think about it – there is

just 10% chance for the option to expire ITM or in other words there is 90% chance

for the option to expire as an OTM option. With such a huge probability favoring the

seller, one should go ahead and take the trade with conviction!

In the same line – what would be the delta of an ITM option? Close to 1 right? So this

means there is a very high probability for an already ITM option to expire as ITM. In

other words the probability of an ITM option expiring OTM is very low, so beware

while shorting/writing ITM options as the odds are already against you!

Remember smart trading is all about taking trades wherein the odds favor you, and

to know if the odds favor you, you certainly need to know your numbers and don

your ‘Model Thinking’ hat.

And with this I hope you have developed a fair understanding on the very first

Option Greek – The delta.

The Gamma beckons us now.

Key takeaways from this chapter

1. The delta is additive in nature

2. The delta of a futures contract is always 1

3. Two ATM option is equivalent to owning 1 futures contract

4. The options contract is not really a surrogate for the futures contract

5. The delta of an option is also the probability for the option to expire ITM

113

Module 5 — Options Theory for Professional Trading

Chapter 12

Gamma (Part 1)

12.1 – The other side of the mountain

How many of you remember your high school calculus? Does the word

differentiation and integration ring a bell? The word ‘Derivatives’ meant something

else to all of us back then – it simply referred to solving lengthy differentiation and

integration problems.

Let me attempt to refresh your memory – the idea here is to just drive a certain

point across and not really get into the technicalities of solving a calculus problem.

Please note, the following discussion is very relevant to options, so please do read

on.

Consider this –

A car is set into motion; it starts from 0 kms travels for 10 minutes and reaches the

kilometer mark. From the 3

kilometer mark, the car travels for another 5

minutes and reaches the 7

kilometer mark.

Let us focus and note what really happens between the 3

and 7

kilometer, –

1. Let ‘x’ = distance, and ‘dx’ the change in distance

2. Change in distance i.e. ‘dx’, is 4 (7 – 3)

3. Let ‘t’ = time, and ‘dt’ the change in time

4. Change in time i.e. ‘dt’, is 5 (15 – 10)

If we divide dx over dt i.e. change in distance over change in time we get ‘Velocity’

(V)!

V = dx / dt

= 4/5

This means the car is travelling 4Kms for every 5 Minutes. Here the velocity is being

expressed in Kms travelled per minute, clearly this is not a convention we use in our

114

day to day conversation as we are used to express speed or velocity in Kms

travelled per hour (KMPH).

We can convert 4/5 to KMPH by making a simple mathematical adjustment –

5 minutes when expressed in hours equals 5/60 hours, plugging this back in the

above equation

= 4 / (5/ 60)

= (4*60)/5

= 48 Kmph

Hence the car is moving at a velocity of 48 kmph (kilometers per hour).

Do remember Velocity is change in distance travelled divided over change in

time. In the calculus world, the Speed or Velocity is called the ‘1

order derivative’

of distance travelled.

Now, let us take this example forward – In the 1

leg of the journey the car reached

the 7

Kilometer after 15 minutes. Further assume in the 2

leg of journey, starting

from the 7

kilometer mark the car travels for another 5 minutes and reaches the

kilometer mark.

We know the velocity of the car in the first leg was 48 kmph, and we can easily

calculate the velocity for the 2

leg of the journey as 96 kmph (here dx = 8 and dt =

5).

It is quite obvious that the car travelled twice as fast in the 2

leg of the journey.

Let us call the change in velocity as ‘dv’. Change in velocity as we know is also called

‘Acceleration’.

We know the change in velocity is

= 96KMPH – 48 KMPH

= 48 KMPH /??

The above answer suggests that the change in velocity is 48 KMPH…. but over what?

Confusing right?

Let me explain –

115

** The following explanation may seem like a digression from the main topic about

Gamma, but it is not, so please read on, if not for anything it will refresh your high school

physics **

When you want to buy a new car, the first thing the sales guy tells you is something

like this – “the car is really fast as it can accelerate 0 to 60 in 5 seconds”. Essentially

he is telling you that the car can change velocity from 0 KMPH (from the state of

complete rest) to 60 KMPH in 5 seconds. Change in velocity here is 60KMPH (60 –

0) over 5 seconds.

Likewise in the above example we know the change in velocity is 48KMPH but over

what? Unless we answer “over what” part, we would not know what the acceleration

really is.

To find out the acceleration in this particular case, we can make some assumptions

–

1. Acceleration is constant

2. We can ignore the 7

kilometer mark for time being – hence we consider the fact

that the car was at 3

kilometer mark at the 10

minute and it reached the

kilometer mark at the 20

minute

Using the above information, we can further deduce more information (in the

calculus world, these are called the ‘initial conditions’).

o Velocity @ the 10

minute (or 3

kilometer mark) = 0 KMPS. This is called the initial

velocity

o Time lapsed @ the 3

kilometer mark = 10 minutes

o Acceleration is constant between the 3

and 15

kilometer mark

o Time at 15

kilometer mark = 20 minutes

o Velocity @ 20

minute (or 15

kilometer marks) is called ‘Final Velocity”

o While we know the initial velocity was 0 kmph, we do not know the final velocity

o Total distance travelled = 15 – 3 = 12 kms

o Total driving time = 20 -10 = 10 minutes

o Average speed (velocity) = 12/10 = 1.2 kmps per minute or in terms of hours it would

be 72 kmph

Now think about this, we know –

116

o Initial velocity = 0 kmph

o Average velocity = 72 kmph

o Final velocity =??

By reverse engineering we know the final velocity should be 144 Kmph as the

average of 0 and 144 is 72.

Further we know acceleration is calculated as = Final Velocity / time (provided

acceleration is constant).

Hence the acceleration is –

= 144 kmph / 10 minutes

10 minutes when converted to hours is (10/60) hours, plugging this back in the

above equation

= 144 kmph / (10/60) hour

= 864 Kilometers per hour.

This means the car is gaining a speed of 864 kilometers every hour, and if a

salesman is selling you this car, he would say the car can accelerate 0 to 72kmph in

5 secs (I’ll let you do this math).

We simplified this problem a great deal by making one assumption – acceleration is

constant. However in reality acceleration is not constant, you accelerate at different

speeds for obvious reasons. Generally speaking, to calculate such

problems involving change in one variable due to the change in another

variable one would have to dig into derivative calculus, more precisely one needs to

use the concept of ‘differential equations’.

Now just think about this for a moment –

We know change in distance travelled (position) = Velocity, this is also called the

order derivative of distance position.

Change in Velocity = Acceleration

Acceleration = Change in Velocity over time, which is in turn the change in position

over time.

Hence it is apt to call Acceleration as the 2

order derivative of the position or the

derivative of Velocity!

Keep this point about the 1

order derivative and 2

order derivative in perspective

as we now proceed to understand the Gamma.

117

12.2 – Drawing Parallels

Over the last few chapters we understood how Delta of an option works. Delta as

we know represents the change in premium for the given change in the underlying

price.

For example if the Nifty spot value is 8000, then we know the 8200 CE option is

OTM, hence its delta could be a value between 0 and 0.5. Let us fix this to 0.2 for the

sake of this discussion.

Assume Nifty spot jumps 300 points in a single day, this means the 8200 CE is no

longer an OTM option, rather it becomes slightly ITM option and therefore by virtue

of this jump in spot value, the delta of 8200 CE will no longer be 0.2, it would be

somewhere between 0.5 and 1.0, let us assume 0.8.

With this change in underlying, one thing is very clear – the delta itself changes.

Meaning delta is a variable, whose value changes based on the changes in the

underlying and the premium! If you notice, Delta is very similar to velocity whose

value changes with change in time and the distance travelled.

The Gamma of an option measures this change in delta for the given change in the

underlying. In other words Gamma of an option helps us answer this question – “For

a given change in the underlying, what will be the corresponding change in the delta

of the option?”

Now, let us re-plug the velocity and acceleration example and draw some parallels

to Delta and Gamma.

order Derivative

o Change in distance travelled (position) with respect to change in time is captured by

velocity, and velocity is called the 1

order derivative of position

118

o Change in premium with respect to change in underlying is captured by delta, and

hence delta is called the 1

order derivative of the premium

order Derivative

o Change in velocity with respect to change in time is captured by acceleration, and

acceleration is called the 2

order derivative of position

o Change in delta is with respect to change in the underlying value is captured by

Gamma, hence Gamma is called the 2

order derivative of the premium

As you can imagine, calculating the values of Delta and Gamma (and in fact all other

Option Greeks) involves number crunching and heavy use of calculus (differential

equations and stochastic calculus).

Here is a trivia for you – as we know, derivatives are called derivatives because the

derivative contracts derives its value based on the value of its respective underlying.

This value that the derivatives contracts derive from its respective underlying is

measured using the application of “Derivatives” as a mathematical concept, hence

the reason why Futures & Options are referred to as ‘Derivatives’ .

You may be interested to know there is a parallel trading universe out there where

traders apply derivative calculus to find trading opportunities day in and day out. In

the trading world, such traders are generally called ‘Quants’, quite a fancy

nomenclature I must say. Quantitative trading is what really exists on the other side

of this mountain called ‘Markets’.

From my experience, understanding the 2

order derivative such as Gamma is not

an easy task, although we will try and simplify it as much as possible in the

subsequent chapters.

Key takeaways from this chapter

1. Financial derivatives are called Financial derivatives because of its dependence on

calculus and differential equations (generally called Derivatives)

2. Delta of an option is a variable and changes for every change in the underlying and

premium

3. Gamma captures the rate of change of delta, it helps us get an answer for a

question such as “What is the expected value of delta for a given change in

underlying”

4. Delta is the 1

order derivative of premium

5. Gamma is the 2

order derivative of premium

119

Module 5 — Options Theory for Professional Trading

Chapter 13

Gamma (Part 2)

129

13.1 – The Curvature

We now know for a fact that the Delta of an option is a variable, as it constantly

changes its value relative to the change in the underlying. Let me repost the graph

of the delta’s movement here –

120

If you look at the blue line representing the delta of a call option, it is quite clear that

it traverses between 0 and 1 or maybe from 1 to 0 as the situation would demand.

Similar observations can be made on the red line representing the put option’s delta

(except the value changes between 0 to -1). This graph reemphasizes what we

already know i.e the delta is a variable and it changes all the time. Given this, the

question that one needs to answer is –

1. I know the delta changes, but why should I care about it?

2. If the change in delta really matters, how do I estimate the likely change in delta?

We will talk about the 2

question first as I’m reasonably certain the answer to the

first question will reveal itself as we progress through this chapter.

As introduced in the previous chapter, ‘The Gamma’ (2

order derivative of

premium) also referred to as the curvature of the option gives the rate at which

the option’s delta changes as the underlying changes. The gamma is usually

expressed in deltas gained or lost per one point change in the underlying – with the

delta increasing by the amount of the gamma when the underlying rises and falling

by the amount of the gamma when the underlying falls.

For example consider this –

o Nifty Spot = 8326

o Strike = 8400

o Option type = CE

o Moneyness of Option = Slightly OTM

o Premium = Rs.26/-

o Delta = 0.3

o Gamma = 0.0025

o Change in Spot = 70 points

o New Spot price = 8326 + 70 = 8396

o New Premium =??

o New Delta =??

o New moneyness =??

Let’s figure this out –

o Change in Premium = Delta * change in spot i.e 0.3 * 70 = 21

o New premium = 21 + 26 = 47

o Rate of change of delta = 0.0025 units for every 1 point change in underlying

o Change in delta = Gamma * Change in underlying i.e 0.0025*70 = 0.175

o New Delta = Old Delta + Change in Delta i.e 0.3 + 0.175 = 0.475

121

o New Moneyness = ATM

When Nifty moves from 8326 to 8396, the 8400 CE premium changed from Rs.26 to

Rs.47, and along with this the Delta changed from 0.3 to 0.475.

Notice with the change of 70 points, the option transitions from slightly OTM to ATM

option. Which means the option’s delta has to change from 0.3 to somewhere close

to 0.5. This is exactly what’s happening here.

Further let us assume Nifty moves up another 70 points from 8396; let us see what

happens with the 8400 CE option –

o Old spot = 8396

o New spot value = 8396 + 70 = 8466

o Old Premium = 47

o Old Delta = 0.475

o Change in Premium = 0.475 * 70 = 33.25

o New Premium = 47 + 33.25 = 80.25

o New moneyness = ITM (hence delta should be higher than 0.5)

o Change in delta =0.0025 * 70 = 0.175

o New Delta = 0.475 + 0.175 = 0.65

Let’s take this forward a little further, now assume Nifty falls by 50 points, let us see

what happens with the 8400 CE option –

o Old spot = 8466

o New spot value = 8466 – 50 = 8416

o Old Premium = 80.25

o Old Delta = 0.65

o Change in Premium = 0.65 *(50) = – 32.5

o New Premium = 80.25 – 32. 5 = 47.75

o New moneyness = slightly ITM (hence delta should be higher than 0.5)

o Change in delta = 0.0025 * (50) = – 0.125

o New Delta = 0.65 – 0.125 = 0.525

Notice how well the delta transitions and adheres to the delta value rules we

discussed in the earlier chapters. Also, you may wonder why the Gamma value is

kept constant in the above examples. Well, in reality the Gamma also changes with

the change in the underlying. This change in Gamma due to changes in underlying is

captured by 3

derivative of underlying called “Speed” or “Gamma of Gamma” or

“DgammaDspot”. For all practical purposes, it is not necessary to get into the

discussion of Speed, unless you are mathematically inclined or you work for an

Investment Bank where the trading book risk can run into several $ Millions.

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Unlike the delta, the Gamma is always a positive number for both Call and Put

Option. Therefore when a trader is long options (both Calls and Puts) the trader is

considered ‘Long Gamma’ and when he is short options (both calls and puts) he is

considered ‘Short Gamma’.

For example consider this – The Gamma of an ATM Put option is 0.004, if the

underlying moves 10 points, what do you think the new delta is?

Before you proceed I would suggest you spend few minutes to think about the

solution for the above.

Here is the solution – Since we are talking about an ATM Put option, the Delta must

be around – 0.5. Remember Put options have a –ve Delta. Gamma as you notice is a

positive number i.e +0.004. The underlying moves by 10 points without specifying

the direction, so let us figure out what happens in both cases.

Case 1 – Underlying moves up by 10 points

o Delta = – 0.5

o Gamma = 0.004

o Change in underlying = 10 points

o Change in Delta = Gamma * Change in underlying = 0.004 * 10 = 0.04

o New Delta = We know the Put option loses delta when underlying increases, hence –

0.5 + 0.04 = – 0.46

Case 2 – Underlying goes down by 10 points

o Delta = – 0.5

o Gamma = 0.004

o Change in underlying = – 10 points

o Change in Delta = Gamma * Change in underlying = 0.004 * – 10 = – 0.04

o New Delta = We know the Put option gains delta when underlying goes down, hence

– 0.5 + (-0.04) = – 0.54

Now, here is trick question for you – In the earlier chapters, we had discussed that

the Delta of the Futures contract in always 1, so what do you think the gamma of

the Futures contract is? Please leave your answers in the comment box below :).

13.2 – Estimating Risk using Gamma

I know there are many traders who define their risk limits while trading. Here is

what I mean by a risk limit – for example the trader may have a capital of

Rs.300,000/- in his trading account. Margin required for each Nifty Futures is

approximately Rs.16,500/-. Do note you can use Zerodha’s SPAN calculator to

figure out the margin required for any F&O contract. So considering the margin and

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the M2M margin required, the trader may decide at any point he may not want to

exceed holding more than 5 Nifty Futures contracts, thus defining his risk limits,

this seems fair enough and works really well while trading futures.

But does the same logic work while trading options? Let’s figure out if it is the right

way to think about risk while trading options.

Here is a situation –

o Number of lots traded = 10 lots (Note – 10 lots of ATM contracts with delta of 0.5

each is equivalent to 5 Futures contract)

o Option = 8400 CE

o Spot = 8405

o Delta = 0.5

o Gamma = 0.005

o Position = Short

The trader is short 10 lots of Nifty 8400 Call Option; this means the trader is within

his risk boundary. Recall the discussion we had in the Delta chapter about adding

up the delta. We can essentially add up the deltas to get the overall delta of the

position. Also each delta of 1 represents 1 lot of the underlying. So we will keep this

in perspective and we can figure out the overall position’s delta.

o Delta = 0.5

o Number of lots = 10

o Position Delta = 10 * 0.5 = 5

So from the overall delta perspective the trader is within his risk boundary of

trading not more than 5 Futures lots. Also, do note since the trader is short options,

he is essentially short gamma.

The position’s delta of 5 indicates that the trader’s position will move 5 points for

every 1 point movement in the underlying.

Now, assume Nifty moves 70 points against him and the trader continues to hold

his position, hoping for a recovery. The trader is obviously under the impression

that he is holding 10 lots of options which is within his risk appetite…

Let’s do some forensics to figure out behind the scenes changes –

o Delta = 0.5

o Gamma = 0.005

o Change in underlying = 70 points

o Change in Delta = Gamma * change in underlying = 0.005 * 70 = 0.35

o New Delta = 0.5 + 0.35 = 0.85

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o New Position Delta = 0.85*10 = 8.5

Do you see the problem here? Although the trader has defined his risk limit of 5

lots, thanks to a high Gamma value, he has overshot his risk limit and now holds

positions equivalent to 8.5 lots, way beyond his perceived risk limit. An

inexperienced trader can be caught unaware of this and still be under the

impression that he is well under his risk radar. But in reality his risk exposure is

getting higher.

Now since the delta is 8.5, his overall position is expected to move 8.5 points for

every 1 point change in the underlying. For a moment assume the trader is long on

the call option instead of being short – obviously he would enjoy the situation here

as the market is moving in his favor. Besides the favorable movement in the market,

his positions is getting ‘Longer’ since the ‘long gamma’ tends to add up the deltas,

and therefore the delta tends to get bigger, which means the rate of change on

premium with respect to change in underlying is faster.

Suggest you read that again in small bits if you found it confusing.

But since the trader is short, he is essentially short gamma…this means when the

position moves against him (as in the market moves up while he is short) the deltas

add up (thanks to gamma) and therefore at every stage of market increase, the

delta and gamma gang up against the short option trader, making his position

riskier way beyond what the plain eyes can see. Perhaps this is the reason why they

say – shorting options carry huge amount of risk. In fact you can be more precise

and say “shorting options carries the risk of being short gamma”.

Note – By no means I’m suggesting that you should not short options. In fact a

successful trader employs both short and long positions as the situation demands.

I’m only suggesting that when you short options you need to be aware of the Greeks

and what they can do to your positions.

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Also, I’d strongly suggest you avoid shorting option contracts which has a large

Gamma.

This leads us to another interesting topic – what is considered as ‘large gamma’.

13.3 – Gamma movement

Earlier in the chapter we briefly discussed that the Gamma changes with respect to

change in the underlying. This change in Gamma is captured by the 3

order

derivative called ‘Speed’. I won’t get into discussing ‘Speed’ for reasons stated earlier.

However we need to know the behavior of Gamma movement so that we can avoid

initiating trades with high Gamma. Of course there are other advantages of

knowing the behavior of Gamma, we will talk about this at a later stage in this

module. But for now we will look into how the Gamma behaves with respect to

changes in the underlying.

Have a look at the chart below,

The chart above has 3 different CE strike prices – 80, 100, and 120 and their

respective Gamma movement. For example the blue line represents the Gamma of

the 80 CE strike price. I would suggest you look at each graph individually to avoid

confusion. In fact for sake of simplicity I will only talk about the 80 CE strike option,

represented by the blue line.

Let us assume the spot price is at 80, thus making the 80 strike ATM. Keeping this in

perspective we can observe the following from the above chart –

1. Since the strike under consideration is 80 CE, the option attains ATM status when

the spot price equals 80

2. Strike values below 80 (65, 70, 75 etc) are ITM and values above 80 (85, 90, 95 etx)

are OTM options.

3. Notice the gamma value is low for OTM Options (80 and above). This explains why

the premium for OTM options don’t change much in terms of absolute point terms,

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however in % terms the change is higher. For example – the premium of an OTM

option can change from Rs.2 to Rs.2.5, while absolute change in is just 50 paisa, the

% change is 25%.

4. The gamma peaks when the option hits ATM status. This implies that the rate of

change of delta is highest when the option is ATM. In other words, ATM options are

most sensitive to the changes in the underlying

1. Also, since ATM options have highest Gamma – avoid shorting ATM options

5. The gamma value is also low for ITM options (80 and below). Hence for a certain

change in the underlying, the rate of change of delta for an ITM option is much

lesser compared to ATM option. However do remember the ITM option inherently

has a high delta. So while ITM delta reacts slowly to the change in underlying (due to

low gamma) the change in premium is high (due to high base value of delta).

6. You can observe similar Gamma behavior for other strikes i.e 100, and 120. In fact

the reason to show different strikes is to showcase the fact that the gamma behaves

in the same way for all options strikes

Just in case you found the above discussion bit overwhelming, here are 3 simple

points that you can take home –

o Delta changes rapidly for ATM option

o Delta changes slowly for OTM and ITM options

o Never short ATM or ITM option with a hope that they will expire worthless upon

expiry

o OTM options are great candidates for short trades assuming you intend to hold

these short trades upto expiry wherein you expect the option to expire worthless

13.4 – Quick note on Greek interactions

One of the keys to successful options trading is to understand how the individual

option Greeks behave under various circumstances. Now besides understanding

the individual Greek behavior, one also needs to understand how these individual

option Greeks react with each other.

So far we have considered only the premium change with respect to the changes in

the spot price. We have not yet discussed time and volatility. Think about the

markets and the real time changes that happen. Everything changes – time,

volatility, and the underlying price. So an option trader should be in a position to

understand these changes and its overall impact on the option premium.

You will fully appreciate this only when you understand the cross interactions of the

option Greeks. Typical Greek cross interactions would be – gamma versus time,

gamma versus volatility, volatility vs time, time vs delta etc.

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Finally all your understanding of the Greeks boils down to a few critical decision

making factors such as –

1. For the given market circumstances which is the best strike to trade?

2. What is your expectation of the premium of that particular strike – would it increase

or decrease? Hence would you be a buyer or a seller in that option?

3. If you plan to buy an option – is there a realistic chance for the premium to

increase?

4. If you plan to short an option – is it really safe to do so? Are you able to see risk

beyond what the naked eyes can spot?

The answers to all these questions will evolve once you fully understand individual

Greeks and their cross interactions.

Given this, here is how this module will develop going further –

1. So far we have understood Delta and Gamma

2. Over the next few chapters we will understand Theta and Vega

3. When we introduce Vega (change in premium with respect to change in volatility) –

we will digress slightly to understand volatility based stoploss

4. Introduce Greek cross interactions – Gamma vs time, Gamma vs spot, Theta vs

Vega, Vega vs Spot etc

5. Overview of Black and Scholes option pricing formula

6. Option calculator

So as you see, we have miles to walk before we sleep .

Key takeaways from this chapter

1. Gamma measures the rate of change of delta

2. Gamma is always a positive number for both Calls and Puts

3. Large Gamma can translate to large gamma risk (directional risk)

4. When you buy options (Calls or Puts) you are long Gamma

5. When you short options (Calls or Puts) you are short Gamma

6. Avoid shorting options which have large gamma

7. Delta changes rapidly for ATM option

8. Delta changes slowly for OTM and ITM options

Special thanks to our good friend Prakash Lekkala for providing the Greek graphs in this

and other chapters

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Module 5 — Options Theory for Professional Trading

Chapter 14

Theta

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14.1 – Time is money

Remember the adage “Time is money”, it seems like this adage about time is highly

relevant when it comes to options trading. Forget all the Greek talk for now, we shall

go back to understand one basic concept concerning time. Assume you have

enrolled for a competitive exam, you are inherently a bright candidate and have the

capability to clear the exam, however if you do not give it sufficient time and brush

up the concepts, you are likely to flunk the exam – so given this what is the

likelihood that you will pass this exam? Well, it depends on how much time you

spend to prepare for the exam right? Let’s keep this in perspective and figure out

the likelihood of passing the exam against the time spent preparing for the exam.

Number of days for preparation

Likelihood of passing

30 days

Very high

20 days

High

15 days

Moderate

10 days

Low

5 days

Very low

1 day

Ultra low

Quite obviously higher the number of days for preparation, the higher is the

likelihood of passing the exam. Keeping the same logic in mind, think about the

following situation – Nifty Spot is 8500, you buy a Nifty 8700 Call option – what is the

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likelihood of this call option to expire In the Money (ITM)? Let me rephrase this

question in the following way –

o Given Nifty is at 8500 today, what is the likelihood of Nifty moving 200 points over

the next 30 days and therefore 8700 CE expiring ITM?

o The chance for Nifty to move 200 points over next 30 days is quite high, hence the

likelihood of option expiring ITM upon expiry is very high

o What if there are only 15 days to expiry?

o An expectation that Nifty will move 200 points over the next 15 days is reasonable,

hence the likelihood of option expiring ITM upon expiry is high (notice it is not very

high, but just high).

o What if there are only 5 days to expiry?

o Well, 5 days, 200 points, not really sure hence the likelihood of 8700 CE expiring in

the money is low

o What if there was only 1 day to expiry?

o The probability of Nifty to move 200 points in 1 day is quite low, hence I would be

reasonably certain that the option will not expire in the money, therefore the

chance is ultra low.

Is there anything that we can infer from the above? Clearly, the more time for expiry

the likelihood for the option to expire In the Money (ITM) is higher. Now keep this

point in the back of your mind as we now shift our focus on the ‘Option Seller’. We

know an option seller sells/writes an option and receives the premium for it. When

he sells an option he is very well aware that he carries an unlimited risk and limited

reward potential. The reward is limited to the extent of the premium he receives. He

gets to keep his reward (premium) fully only if the option expires worthless. Now,

think about this – if he is selling an option early in the month he very clearly knows

the following –

1. He knows he carries unlimited risk and limited reward potential

2. He also knows that by virtue of time, there is a chance for the option he is selling to

transition into ITM option, which means he will not get to retain his reward

(premium received)

In fact at any given point, thanks to ‘time’, there is always a chance for the option to

expiry in the money (although this chance gets lower and lower as time progresses

towards the expiry date). Given this, an option seller would not want to sell options

at all right? After all why would you want to sell options when you very well know

that simply because of time there is scope for the option you are selling to expire in

the money. Clearly time in the option sellers context acts as a risk. Now, what if the

option buyer in order to entice the option seller to sell options offers to compensate

for the ‘time risk’ that he (option seller) assumes? In such a case it probably makes

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sense to evaluate the time risk versus the compensation and take a call right? In fact

this is what happens in real world options trading. Whenever you pay a premium for

options, you are indeed paying towards –

1. Time Risk

2. Intrinsic value of options.

In other words – Premium = Time value + Intrinsic Value Recall earlier in this

module we defined ‘Intrinsic Value’ as the money you are to receive, if you were to

exercise your option today. Just to refresh your memory, let us calculate the intrinsic

value for the following options assuming Nifty is at 8423 –

1. 8350 CE

2. 8450 CE

3. 8400 PE

4. 8450 PE

We know the intrinsic value is always a positive value or zero and can never be

below zero. If the value turns out to be negative, then the intrinsic value is

considered zero. We know for Call options the intrinsic value is “Spot Price – Strike

Price” and for Put options it is “Strike Price – Spot Price”. Hence the intrinsic values

for the above options are as follows –

1. 8350 CE = 8423 – 8350 = +73

2. 8450 CE = 8423 – 8450 = -ve value hence 0

3. 8400 PE = 8400 – 8423 = -ve value hence 0

4. 8450 PE = 8450 – 8423 = + 27

So given that we know how to calculate the intrinsic value of an option, let us

attempt to decompose the premium and extract the time value and intrinsic value.

Have a look at the following snapshot –

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Details to note are as follows –

o Spot Value = 8531

o Strike = 8600 CE

o Status = OTM

o Premium = 99.4

o Today’s date = 6

July 2015

o Expiry = 30

July 2015

Intrinsic value of a call option – Spot Price – Strike Price i.e 8531 – 8600 = 0 (since it’s

a negative value) We know – Premium = Time value + Intrinsic value 99.4 = Time

Value + 0 This implies Time value = 99.4! Do you see that? The market is willing to

pay a premium of Rs.99.4/- for an option that has zero intrinsic value but ample

time value! Recall time is money Here is snapshot of the same contract that I

took the next day i.e 7

July –

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Notice the underlying value has gone up slightly (8538) but the option premium has

decreased quite a bit! Let’s decompose the premium into its intrinsic value and time

value – Spot Price – Strike Price i.e 8538 – 8600 = 0 (since it’s a negative value) We

know – Premium = Time value + Intrinsic value 87.9 = Time Value + 0 This implies

Time value = 87.9! Notice the overnight drop in premium value? We will soon

understand why this happened. Note – In this example, the drop in premium value

is 99.4 minus 87.9 = 11.5. This drop is attributable to drop in volatility and time.

We will talk about volatility in the next chapter. For the sake of argument, if both

volatility and spot were constant, the drop in premium would be completely

attributable to the passage of time. I would suspect this drop would be around Rs.5

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or so and not really Rs.11.5/-. Let us take another example –

o Spot Value = 8514.5

o Strike = 8450 CE

o Status = ITM

o Premium = 160

o Today’s date = 7

July 2015

o Expiry = 30

July 2015

Intrinsic value of call option – Spot Price – Strike Price i.e 8514.5 – 8450 = 64.5 We

know – Premium = Time value + Intrinsic value 160 = Time Value + 64.5 This implies

the Time value = 160 – 64.5 = 95.5 Hence out of the total premium of Rs.160, traders

are paying 64.5 towards intrinsic value and 95.5 towards the time value. You can

repeat the calculation for all options (both calls and puts) and decompose the

premium into the Time value and intrinsic value.

14.2 – Movement of time

Time as we know moves in one direction. Keep the expiry date as the target time

and think about the movement of time. Quite obviously as time progresses, the

number of days for expiry gets lesser and lesser. Given this let me ask you this

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question – With roughly 18 trading days to expiry, traders are willing to pay as much

as Rs.100/- towards time value, will they do the same if time to expiry was just 5

days? Obviously they would not right? With lesser time to expiry, traders will pay a

much lesser value towards time. In fact here is a snap shot that I took from the

earlier months –

o Date = 29

April

o Expiry Date = 30

April

o Time to expiry = 1 day

o Strike = 190

o Spot = 179.6

o Premium = 30 Paisa

o Intrinsic Value = 179.6 – 190 = 0 since it’s a negative value

o Hence time value should be 30 paisa which equals the premium

With 1 day to expiry, traders are willing to pay a time value of just 30 paisa.

However, if the time to expiry was 20 days or more the time value would probably

be Rs.5 or Rs.8/-. The point that I’m trying to make here is this – with every passing

day, as we get closer to the expiry day, the time to expiry becomes lesser and lesser.

This means the option buyers will pay lesser and lesser towards time value. So if the

option buyer pays Rs.10 as the time value today, tomorrow he would probably pay

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Rs.9.5/- as the time value. This leads us to a very important conclusion – “All other

things being equal, an option is a depreciating asset. The option’s premium

erodes daily and this is attributable to the passage of time”. Now the next

logical question is – by how much would the premium decrease on a daily basis

owing to the passage of time? Well, Theta the 3

Option Greek helps us answer this

question.

14.3 – Theta

All options – both Calls and Puts lose value as the expiration approaches. The Theta

or time decay factoris the rate at which an option loses value as time passes. Theta

is expressed in points lost per day when all other conditions remain the same. Time

runs in one direction, hence theta is always a positive number, however to remind

traders it’s a loss in options value it is sometimes written as a negative number. A

Theta of -0.5 indicates that the option premium will lose -0.5 points for every day

that passes by. For example, if an option is trading at Rs.2.75/- with theta of -0.05

then it will trade at Rs.2.70/- the following day (provided other things are kept

constant). A long option (option buyer) will always have a negative theta meaning all

else equal, the option buyer will lose money on a day by day basis. A short option

(option seller) will have a positive theta. Theta is a friendly Greek to the option seller.

Remember the objective of the option seller is to retain the premium. Given that

options loses value on a daily basis, the option seller can benefit by retaining the

premium to the extent it loses value owing to time. For example if an option writer

has sold options at Rs.54, with theta of 0.75, all else equal, the same option is likely

to trade at – =0.75 * 3 = 2.25 = 54 – 2.25 = 51.75 Hence the seller can choose to close

the option position on T+ 3 day by buying it back at Rs.51.75/- and profiting Rs.2.25

…and this is attributable to theta! Have a look at the graph below –

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This is the graph of how premium erodes as time to expiry approaches. This is also

called the ‘Time Decay’graph. We can observe the following from the graph –

1. At the start of the series – when there are many days for expiry the option does not

lose much value. For example when there were 120 days to expiry the option was

trading at 350, however when there was 100 days to expiry, the option was trading

at 300. Hence the effect of theta is low

2. As we approach the expiry of the series – the effect of theta is high. Notice when

there was 20 days to expiry the option was trading around 150, but when we

approach towards expiry the drop in premium seems to accelerate (option value

drops below 50).

So if you are selling options at the start of the series – you have the advantage of

pocketing a large premium value (as the time value is very high) but do remember

the fall in premium happens at a low rate. You can sell options closer to the expiry –

you will get a lower premium but the drop in premium is high, which is

advantageous to the options seller. Theta is a relatively straightforward and easy

Greek to understand. We will revisit theta again when we will discuss cross

dependencies of Greeks. But for now, if you have understood all that’s being

discussed here you are good to go. We shall now move forward to understand the

last and the most interesting Greek – Vega!

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Key takeaways from this chapter

1. Option sellers are always compensated for the time risk

2. Premium = Intrinsic Value + Time Value

3. All else equal, options lose money on a daily basis owing to Theta

4. Time moves in a single direction hence Theta is a positive number

5. Theta is a friendly Greek to option sellers

6. When you short naked options at the start of the series you can pocket a large time

value but the fall in premium owing to time is low

7. When you short option close to expiry the premium is low (thanks to time value) but

the fall in premium is rapid

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Module 5 — Options Theory for Professional Trading

Chapter 15

Volatility Basics

15.1 – Background

Having understood Delta, Gamma, and Theta we are now at all set to explore one of

the most interesting Option Greeks – The Vega. Vega, as most of you might have

guessed is the rate of change of option premium with respect to change in volatility.

But the question is – What is volatility? I have asked this question to quite a few

traders and the most common answer is “Volatility is the up down movement of the

stock market”. If you have a similar opinion on volatility, then it is about time we

fixed that .

So here is the agenda, I suppose this topic will spill over a few chapters –

1. We will understand what volatility really means

2. Understand how to measure volatility

3. Practical Application of volatility

4. Understand different types of volatility

5. Understand Vega

So let’s get started.

15.2 – Moneyball

Have you watched this Hollywood movie called ‘Moneyball’? It’s a real life story Billy

Beane – manager of a base ball team in US. The movie is about Billy Beane and his

young colleague, and how they leverage the power of statistics to identify relatively

low profile but extremely talented baseball players. A method that was unheard of

during his time, and a method that proved to be both innovative and disruptive.

You can watch the trailer of Moneyball here.

I love this movie, not just for Brad Pitt, but for the message it drives across on topics

related to life and business. I will not get into the details now, however let me draw

some inspiration from the Moneyball method, to help explain volatility :).

The discussion below may appear unrelated to stock markets, but please don’t get

discouraged. I can assure you that it is relevant and helps you relate better to the

term ‘Volatility’.

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Consider 2 batsmen and the number of runs they have scored over 6 consecutive

matches –

Match

Billy

Mike

You are the captain of the team, and you need to choose either Billy or Mike for the

match. The batsman should be dependable – in the sense that the batsman you

choose should be in a position to score at least 20 runs. Whom would you choose?

From my experience I have noticed that people approach this problem in one of the

two ways –

1. Calculate the total score (also called ‘Sigma’) of both the batsman – pick the

batsman with the highest score for next game. Or..

2. Calculate the average (also called ‘Mean’) number of scores per game – pick the

batsman with better average.

Let us calculate the same and see what numbers we get –

o Billy’s Sigma = 20 + 23 + 21 + 24 + 19 + 23 = 130

o Mike’s Sigma = 45 + 13 + 18 + 12 + 26 + 19 = 133

So based on the sigma you are likely to select Mike. Let us calculate the mean or

average for both the players and figure out who stands better –

o Billy = 130/6 = 21.67

o Mike = 133/6 = 22.16

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So it seems from both the mean and sigma perspective, Mike deserves to be

selected. But let us not conclude that yet. Remember the idea is to select a player

who can score at least 20 runs and with the information that we have now (mean

and sigma) there is no way we can conclude who can score at least 20 runs.

Therefore, let’s do some further investigation.

To begin with, for each match played we will calculate the deviation from the mean.

For example, we know Billy’s mean is 21.67 and in his first match Billy scored 20

runs. Therefore deviation from mean form the 1st match is 20 – 21.67 = – 1.67. In

other words, he scored 1.67 runs lesser than his average score. For the 2

match it

was 23 – 21.67 = +1.33, meaning he scored 1.33 runs more than his average score.

Here is the diagram representing the same (for Billy) –

The middle black line represents the average score of Billy, and the double arrowed

vertical line represents the the deviation from mean, for each of the match played.

We will now go ahead and calculate another variable called ‘Variance’.

Variance is simply the ‘sum of the squares of the deviation divided by the total

number of observations’. This may sound scary, but its not. We know the total

number of observations in this case happens to be equivalent to the total number

of matches played, hence 6.

So variance can be calculated as –

Variance = [(-1.67) ^2 + (1.33) ^2 + (-0.67) ^2 + (+2.33) ^2 + (-2.67) ^2 + (1.33) ^2] / 6

= 19.33 / 6

= 3.22

Further we will define another variable called ‘Standard Deviation’ (SD) which is

calculated as –

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std deviation = √ variance

So standard deviation for Billy is –

= SQRT (3.22)

= 1.79

Likewise Mike’s standard deviation works out to be 11.18.

Lets stack up all the numbers (or statistics) here –

Statistics

Billy

Mike

Sigma

130

133

Mean

21.6

22.16

1.79

11.18

We know what ‘Mean’ and ‘Sigma’ signifies, but what about the SD? Standard

Deviation simply generalizes and represents the deviation from the average.

Here is the text book definition of SD “In statistics, the

standard deviation

(SD, also

represented by the Greek letter sigma, σ) is a measure that is used to quantify the

amount of variation or dispersion of a set of data values”.

Please don’t get confused between the two sigma’s – the total is also called sigma

represented by the Greek symbol ∑ and standard deviation is also sometimes

referred to as sigma represented by the Greek symbol σ.

One way to use SD is to make a projection on how many runs Billy and Mike are

likely to score in the next match. To get this projected score, you simply need to add

and subtract the SD from their average.

Player

Lower Estimate

Upper Estimate

Billy

21.6 – 1.79 = 19.81

21.6 + 1.79 = 23.39

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Mike

22.16 – 11.18 = 10.98

22.16 + 11.18 = 33.34

These numbers suggest that in the upcoming 7

match Billy is likely to get a score

anywhere in between 19.81 and 23.39 while Mike stands to score anywhere

between 10.98 and 33.34. Because Mike has a wide range, it is difficult to figure out

if he is going to score at least 20 runs. He can either score 10 or 34 or anything in

between.

However Billy seems to be more consistent. His range is smaller, which means he

will neither be a big hitter nor a lousy player. He is expected to be a consistent and

is likely to score anywhere between 19 and 23. In other words – selecting Mike over

Billy for the 7

match can be risky.

Going back to our original question, which player do you think is more likely to score

at least 20 runs? By now, the answer must be clear; it has to be Billy. Billy is

consistent and less risky compared to Mike.

So in principal, we assessed the riskiness of these players by using “Standard

Deviation”. Hence ‘Standard Deviation’ must represent ‘Risk’. In the stock market

world, we define ‘Volatility’ as the riskiness of the stock or an index. Volatility is a %

number as measured by standard deviation.

I’ve picked the definition of Volatility from Investopedia for you – “A statistical

measure of the dispersion of returns for a given security or market index. Volatility can

either be measured by using the standard deviation or variance between returns from

that same security or market index. Commonly higher the standard deviation, higher is

the risk”.

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Going by the above definition, if Infosys and TCS have volatility of 25% and 45%

respectively, then clearly Infosys has less risky price movements when compared to

TCS.

15.3 – Some food for thought

Before I wrap this chapter, let’s do some prediction –

Today’s Date = 15

July 2015

Nifty Spot = 8547

Nifty Volatility = 16.5%

TCS Spot = 2585

TCS Volatility = 27%

Given this information, can you predict the likely range within which Nifty and TCS

will trade 1 year from now?

Of course we can, let us put the numbers to good use –

Asset

Lower Estimate

Upper Estimate

Nifty

8547 – (16.5% * 8547) = 7136

8547 + (16.5% * 8547) = 9957

TCS

2585 – (27% * 2585) = 1887

2585 + (27% * 2585) = 3282

So the above calculations suggest that in the next 1 year, given Nifty’s volatility, Nifty

is likely to trade anywhere between 7136 and 9957 with all values in between

having varying probability of occurrence. This means to say on 15

July 2016 the

probability of Nifty to be around 7500 could be 25%, while 8600 could be around

40%.

This leads us to a very interesting platform –

1. We estimated the range for Nifty for 1 year; similarly can we estimate the range

Nifty is likely to trade over the next few days or the range within which Nifty is likely

to trade upto the series expiry?

1. If we can do this, then we will be in a better position to identify options that are

likely to expire worthless, meaning we could sell them today and pocket the

premiums.

2. We figured the range in which Nifty is likely to trade in the next 1 year as 7136 and

9957 – but how sure are we? Is there any degree of confidence while expressing this

range?

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3. How do we calculate Volatility? I know we discussed the same earlier in the chapter,

but is there an easier way? Hint – we could use MS Excel!

4. We calculated Nifty’s range estimating its volatility as 16.5% , what if the volatility

changes?

Over the next few chapters we will answer all these questions and more!

Key takeaways from this chapter

1. Vega measures the rate of change of premium with respect to change in volatility

2. Volatility is not just the up down movement of markets

3. Volatility is a measure of risk

4. Volatility is estimated by standard deviation

5. Standard Deviation is the square root of variance

6. We can estimate the range of the stock price given its volatility

7. Larger the range of a stock, higher is its volatility aka risk.

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Module 5 — Options Theory for Professional Trading

Chapter 16

Volatility Calculation (Historical)

227

16.1 – Calculating Volatility on Excel

In the previous chapter, we introduced the concept of standard deviation and how it

can be used to evaluate ‘Risk or Volatility’ of a stock. Before we move any further on

this topic I would like to discuss how one can calculate volatility. Volatility data is not

easily available, hence its always good to know how to calculate the same yourself.

Of course in the previous chapter we looked into this calculation (recall the Billy &

Mike example), we outlined the steps as follows –

1. Calculate the average

2. Calculate the deviation – Subtract the average from the actual observation

3. Square and add up all deviations – this is called variance

4. Calculate the square root of variance – this is called standard deviation

The purpose of doing this in the previous chapter was to show you the mechanics

behind the standard deviation calculation. In my opinion it is important to know

what really goes beyond a formula, it only enhances your insights. In this chapter

however, we will figure out an easier way to calculate standard deviation or the

volatility of a given stock using MS Excel. MS Excel uses the exact same steps we

outlined above, just that it happens at a click of a button.

I’ll give you the border steps involved first and then elaborate on each step –

1. Download the historical data of closing prices

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2. Calculate the daily returns

3. Use the STDEV function

So let us get to work straight away.

Step 1 – Download the historical closing prices

You can do this from any data source that you have. Some of the free and reliable

data sources are NSE India website and Yahoo Finance.

I will take the data from NSE India for now. At this point I must tell you that NSE’s

website is quite resourceful, and in terms of information provided, I guess NSE’s

website is one of the best stock exchange websites in the world.

Anyway, in this chapter let us calculate Wipro’s volatility. To download the historical

closing prices, visit

– http://www.nseindia.com/products/content/equities/equities/equities.htm and

click on historical data and select the search option.

Here is a snapshot where I have highlighted the search option –

Once you hit search, a set of fields open up, filling them up is quite self explanatory

– just fill in the required details and hit ‘Get Data’. Do make sure you get the data for

the last 1 year. The dates that I have selected here is from 22

July 2014 to 21

July

2015.

Once you hit ‘get data’, NSE’s website will query your request and fetch you the

required data. At this point you should see the following screen –

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Once you get this, click on ‘Download file in CSV format’ (highlighted in the green

box), and that’s it.

You now have the required data on Excel. Of course along with the closing prices,

you have tons of other information as well. I usually like to delete all the other

unwanted data and stick to just the date and closing price. This makes the sheet

look clutter free and crisp.

Here is a snapshot of how my excel sheet looks at this stage –

Do note, I have deleted all the unnecessary information. I have retained just the

date and closing prices.

Step 2 – Calculate Daily Returns

We know that the daily returns can be calculated as –

Return = (Ending Price / Beginning Price) – 1

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However for all practical purposes and ease of calculation, this equation can be

approximated to:

Return = LN (Ending Price / Beginning Price), where LN denotes Logarithm to

Base ‘e’, note this is also called ‘Log Returns’.

Here is a snap shot showing you how I’ve calculated the daily log returns of WIPRO –

I have used the Excel function ‘LN’ to calculate the long returns.

Step 3 – Use the STDEV Function

Once the daily returns are calculated, you can use an excel function called ‘STDEV’ to

calculate the standard deviation of daily returns, which if you realize is the daily

Volatility of WIPRO.

Note – In order to use the STDEV function all you need to do is this –

1. Take the cursor an empty cell

2. Press ‘=’

3. Follow the = sign by the function syntax i.e STDEV and open a bracket, hence the

empty cell would look like =STEDEV(

4. After the open bracket, select all the daily return data points and close the bracket

5. Press enter

Here is the snapshot which shows the same –

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Once this is done, Excel will instantly calculate the daily standard deviation aka

volatility of WIPRO for you. I get the answer as 0.0147 which when converted to a

percentage reads as 1.47%.

This means the daily volatility of WIPRO is 1.47% !

The value we have calculated is WIPRO’s daily volatility, but what about its annual

volatility?

Now here is a very important convention you will have to remember – in order to

convert the daily volatility to annual volatility just multiply the daily volatility number

with the square root of time.

Likewise to convert the annual volatility to daily volatility, divide the annual volatility

by square root of time.

So in this case we have calculated the daily volatility, and we now need WIPRO’s

annual volatility. We will calculate the same here –

o Daily Volatility = 1.47%

o Time = 365

o Annual Volatility = 1.47% * SQRT (365)

o = 28.08%

In fact I have calculated the same on excel, have a look at the image below –

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So with this, we know WIPRO’s daily volatility is 1.47% and its annual volatility is

about 28%.

Lets double check these numbers with what the NSE has published on their website.

NSE publishes these numbers only for F&O stocks and not other stocks. Here is the

snapshot of the same –

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Our calculation is pretty much close to what NSE has calculated – as per NSE’s

calculation Wipro’s daily volatility is about 1.34% and Annualized Volatility is about

25.5%.

So why is there a slight difference between our calculation and NSE’s? – One

possible reason could be that we are using spot price while NSE is using Futures

price. However I really don’t want to get into investigating why this slight difference

exists. The agenda here is to know how to calculate the volatility of the security

given its daily returns.

Before we wrap up this chapter, let us just do one more calculation. Assume we

directly get the annual volatility of WIPRO as 25.5%, how do we figure out its daily

volatility?

Like I mentioned earlier, to convert annual volatility to daily volatility you simply

have to divide the annual volatility by the square root of time, hence in this

particular case –

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= 25.5% / SQRT (365)

= 1.34%

So far we have understood what volatility is and how to calculate the same. In the

next chapter we will understand the practical application of volatility.

Do remember we are still in the process of understanding volatility; however the

final objective is to understand the option greek Vega and that really means. So

please do not lose sight of our end objective.

Please click here to download the excel sheet.

Key takeaways from this chapter

1. Standard Deviation represents volatility, which in turn represents risk

2. We can use NSE website to get the daily closing prices of securities

3. Daily return can be calculated as log returns

4. Log function in excel is LN

5. Daily return formula = LN (Today’s Value / Yesterday’s Value) expressed as a

percentage

6. Excel function to calculate volatility is STDEV

7. Standard Deviation of daily return is equivalent of daily volatility

8. To convert daily volatility to annual volatility multiply the daily volatility by the

square root of time

9. Likewise to convert annual volatility to daily volatility, divide the annual volatility by

the square root of time

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Module 5 — Options Theory for Professional Trading

Chapter 17

Volatility & Normal Distribution

214

17.1 – Background

In the earlier chapter we had this discussion about the range within which Nifty is

likely to trade given that we know its annualized volatility. We arrived at an upper

and lower end range for Nifty and even concluded that Nifty is likely to trade within

the calculated range.

Fair enough, but how sure are we about this? Is there a possibility that Nifty would

trade outside this range? If yes, what is the probability that it will trade outside the

range and what is the probability that Nifty will trade within the range? If there is an

outside range, then what are its values?

Finding answers to these questions are very important for several reasons. If not for

anything it will lay down a very basic foundation to a quantitative approach to

markets, which is very different from the regular fundamental and technical analysis

thought process.

So let us dig a bit deeper and get our answers.

17.2 – Random Walk

The discussion we are about to have is extremely important and highly relevant to

the topic at hand, and of course very interesting as well.

Have a look at the image below –

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What you see is called a ‘Galton Board’. A Galton Board has pins stuck to a board.

Collecting bins are placed right below these pins.

The idea is to drop a small ball from above the pins. Moment you drop the ball, it

encounters the first pin after which the ball can either turn left or turn right before it

encounters another pin. The same procedure repeats until the ball trickles down

and falls into one of the bins below.

Do note, once you drop the ball from top, you cannot do anything to artificially

control the path that the ball takes before it finally rests in one of the bins. The path

that the ball takes is completely natural and is not predefined or controlled. For this

particular reason, the path that the ball takes is called the ‘Random Walk’.

Now, can you imagine what would happen if you were to drop several such balls

one after the other? Obviously each ball will take a random walk before it falls into

one of the bins. However what do you think about the distribution of these balls in

the bins?.

o Will they all fall in the same bin? or

o Will they all get distributed equally across the bins? or

o Will they randomly fall across the various bins?

I’m sure people not familiar with this experiment would be tempted to think that the

balls would fall randomly across various bins and does not really follow any

particular pattern. But this does not happen, there seems to be an order here.

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Have a look at the image below –

It appears that when you drop several balls on the Galton Board, with each ball

taking a random walk, they all get distributed in a particular way –

o Most of the balls tend to fall in the central bin

o As you move further away from the central bin (either to the left or right), there are

fewer balls

o The bins at extreme ends have very few balls

A distribution of this sort is called the “Normal Distribution”. You may have heard

of the bell curve from your school days, bell curve is nothing but the normal

distribution. Now here is the best part, irrespective of how many times you repeat

this experiment, the balls always get distributed to form a normal distribution.

This is a very popular experiment called the Galton Board experiment; I would

strongly recommend you to watch this beautiful video to understand this discussion

better –

So why do you think we are discussing the Galton Board experiment and the

Normal Distribution?

Well many things in real life follow this natural order. For example –

o Gather a bunch of adults and measure their weights – segregate the weights across

bins (call them the weight bins) like 40kgs to 50kgs, 50kgs to 60kgs, 60kgs to 70kgs

156

etc. Count the number of people across each bin and you end up getting a normal

distribution

o Conduct the same experiment with people’s height and you will end up getting a

normal distribution

o You will get a Normal Distribution with people’s shoe size

o Weight of fruits, vegetables

o Commute time on a given route

o Lifetime of batteries

This list can go on and on, however I would like to draw your attention to one more

interesting variable that follows the normal distribution – the daily returns of a

stock!

The daily returns of a stock or an index cannot be predicted – meaning if you were

to ask me what will be return on TCS tomorrow I will not be able to tell you, this is

more like the random walk that the ball takes. However if I collect the daily returns

of the stock for a certain period and see the distribution of these returns – I get to

see a normal distribution aka the bell curve!

To drive this point across I have plotted the distribution of the daily returns of the

following stocks/indices –

o Nifty (index)

o Bank Nifty ( index)

o TCS (large cap)

o Cipla (large cap)

o Kitex Garments (small cap)

o Astral Poly (small cap)

157

As you can see the daily returns of the stocks and indices clearly follow a normal

distribution.

Fair enough, but I guess by now you would be curious to know why is this important

and how is it connected to Volatility? Bear with me for a little longer and you will

know why I’m talking about this.

158

17.3 – Normal Distribution

I think the following discussion could be a bit overwhelming for a person exploring

the concept of normal distribution for the first time. So here is what I will do – I will

explain the concept of normal distribution, relate this concept to the Galton board

experiment, and then extrapolate it to the stock markets. I hope this will help you

grasp the gist better.

So besides the Normal Distribution there are other distributions across which data

can be distributed. Different data sets are distributed in different statistical ways.

Some of the other data distribution patterns are – binomial distribution, uniform

distribution, poisson distribution, chi square distribution etc. However the normal

distribution pattern is probably the most well understood and researched

distribution amongst the other distributions.

The normal distribution has a set of characteristics that helps us develop insights

into the data set. The normal distribution curve can be fully described by two

numbers – the distribution’s mean (average) and standard deviation.

The mean is the central value where maximum values are concentrated. This is the

average value of the distribution. For instance, in the Galton board experiment the

mean is that bin which has the maximum numbers of balls in it.

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So if I were to number the bins (starting from the left) as 1, 2, 3…all the way upto 9

(right most), then the 5

bin (marked by a red arrow) is the ‘average’ bin. Keeping the

average bin as a reference, the data is spread out on either sides of this average

reference value. The way the data is spread out (dispersion as it is called) is

quantified by the standard deviation (recollect this also happens to be the volatility

in the stock market context).

Here is something you need to know – when someone says ‘Standard Deviation (SD)’

by default they are referring to the 1

SD. Likewise there is 2

standard deviation

(2SD), 3

standard deviation (SD) etc. So when I say SD, I’m referring to just the

standard deviation value, 2SD would refer to 2 times the SD value, 3 SD would refer

to 3 times the SD value so on and so forth.

For example assume in case of the Galton Board experiment the SD is 1 and

average is 5. Then,

o 1 SD would encompass bins between 4

bin (5 – 1 ) and 6

bin (5 + 1). This is 1 bin to

the left and 1 bin to the right of the average bin

o 2 SD would encompass bins between 3

bin (5 – 2*1) and 7

bin (5 + 2*1)

o 3 SD would encompass bins between 2

bin (5 – 3*1) and 8

bin (5 + 3*1)

Now keeping the above in perspective, here is the general theory around the

normal distribution which you should know –

o Within the 1

standard deviation one can observe 68% of the data

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o Within the 2

standard deviation one can observe 95% of the data

o Within the 3

standard deviation one can observe 99.7% of the data

The following image should help you visualize the above –

Applying this to the Galton board experiment –

o Within the 1

standard deviation i.e between 4

and 6

bin we can observe that 68%

of balls are collected

o Within the 2

standard deviation i.e between 3

and 7

bin we can observe that 95%

of balls are collected

o Within the 3

standard deviation i.e between 2

and 8

bin we can observe that

99.7% of balls are collected

Keeping the above in perspective, let us assume you are about to drop a ball on the

Galton board and before doing so we both engage in a conversation –

You – I’m about to drop a ball, can you guess which bin the ball will fall into?

Me – No, I cannot as each ball takes a random walk. However, I can predict the

range of bins in which it may fall

You – Can you predict the range?

Me – Most probably the ball will fall between the 4

and the 6

bin

You – Well, how sure are you about this?

Me – I’m 68% confident that it would fall anywhere between the 4

and the 6

bin

You – Well, 68% is a bit low on accuracy, can you estimate the range with a greater

accuracy?

161

Me – Sure, I can. The ball is likely to fall between the 3

and 7

bin, and I’m 95% sure

about this. If you want an even higher accuracy then I’d say that the ball is likely to

fall between the 2

and 8

bin and I’m 99.5% sure about this

You – Nice, does that mean there is no chance for the ball to fall in either the 1

bin?

Me – Well, there is certainly a chance for the ball to fall in one of the bins outside

the 3

SD bins but the chance is very low

You – How low?

Me – The chance is as low as spotting a ‘Black Swan’ in a river. Probability wise, the

chance is less than 0.5%

You – Tell me more about the Black Swan

Me – Black Swan ‘events’ as they are called, are events (like the ball falling in 1st or

bin) that have a low probability of occurrence. But one should be aware that

black swan events have a non-zero probability and it can certainly occur – when and

how is hard to predict. In the picture below you can see the occurrence of a black

swan event –

In the above picture there are so many balls that are dropped, but only a handful of

them collect at the extreme ends.

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17.4 – Normal Distribution and stock returns

Hopefully the above discussion should have given you a quick introduction to the

normal distribution. The reason why we are talking about normal distribution is that

the daily returns of the stock/indices also form a bell curve or a normal distribution.

This implies that if we know the mean and standard deviation of the stock return,

then we can develop a greater insight into the behavior of the stock’s returns or its

dispersion. For sake of this discussion, let us take up the case of Nifty and do

some analysis.

To begin with, here is the distribution of Nifty’s daily returns is –

As we can see the daily returns are clearly distributed normally. I’ve calculated the

average and standard deviation for this distribution (in case you are wondering how

to calculate the same, please do refer to the previous chapter). Remember to

calculate these values we need to calculate the log daily returns.

o Daily Average / Mean = 0.04%

o Daily Standard Deviation / Volatility = 1.046%

o Current market price of Nifty = 8337

Do note, an average of 0.04% indicates that the daily returns of nifty are centered at

0.04%. Now keeping this information in perspective let us calculate the following

things –

o The range within which Nifty is likely to trade in the next 1 year

o The range within which Nifty is likely to trade over the next 30 days.

For both the above calculations, we will use 1 and 2 standard deviation meaning

with 68% and 95% confidence.

Solution 1 – (Nifty’s range for next 1 year)

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Average = 0.04%

SD = 1.046%

Let us convert this to annualized numbers –

Average = 0.04*252 = 9.66%

SD = 1.046% * Sqrt (252) = 16.61%

So with 68% confidence I can say that the value of Nifty is likely to be in the range of

–

= Average + 1 SD (Upper Range) and Average – 1 SD (Lower Range)

= 9.66% + 16.61% = 26.66%

= 9.66% – 16.61% = -6.95%

Note these % are log percentages (as we have calculated this on log daily returns),

so we need to convert these back to regular %, we can do that directly and get the

range value (w.r.t to Nifty’s CMP of 8337) –

Upper Range

= 8337 *exponential (26.66%)

= 10841

And for lower range –

= 8337 * exponential (-6.95%)

= 7777

The above calculation suggests that Nifty is likely to trade somewhere between 7777

and 10841. How confident I am about this? – Well as you know I’m 68% confident

about this.

Let us increase the confidence level to 95% or the 2

standard deviation and check

what values we get –

Average + 2 SD (Upper Range) and Average – 2 SD (Lower Range)

= 9.66% + 2* 16.61% = 42.87%

= 9.66% – 2* 16.61% = -23.56%

Hence the range works out to –

Upper Range

= 8337 *exponential (42.87%)

= 12800

And for lower range –

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= 8337 * exponential (-23.56%)

= 6587

The above calculation suggests that with 95% confidence Nifty is likely to trade

anywhere in the range of 6587 and 12800 over the next one year. Also as you can

notice when we want higher accuracy, the range becomes much larger.

I would suggest you do the same exercise for 99.7% confidence or with 3SD and

figure out what kind of range numbers you get.

Now, assume you do the range calculation of Nifty at 3SD level and get the lower

range value of Nifty as 5000 (I’m just quoting this as a place holder number here),

does this mean Nifty cannot go below 5000? Well it certainly can but the chance of

going below 5000 is low, and if it really does go below 5000 then it can be termed as

a black swan event. You can extend the same argument to the upper end range as

well.

Solution 2 – (Nifty’s range for next 30 days)

We know the daily mean and SD –

Average = 0.04%

SD = 1.046%

Since we are interested in calculating the range for next 30 days, we need to convert

the same for the desired time period –

Average = 0.04% * 30 = 1.15%

SD = 1.046% * sqrt (30) = 5.73%

So with 68% confidence I can say that, the value of Nifty over the next 30 days is

likely to be in the range of –

= Average + 1 SD (Upper Range) and Average – 1 SD (Lower Range)

= 1.15% + 5.73% = 6.88%

= 1.15% – 5.73% = – 4.58%

Note these % are log percentages, so we need to convert them back to regular %,

we can do that directly and get the range value (w.r.t to Nifty’s CMP of 8337) –

= 8337 *exponential (6.88%)

= 8930

And for lower range –

= 8337 * exponential (-4.58%)

= 7963

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The above calculation suggests that with 68% confidence level I can estimate Nifty to

trade somewhere between 8930 and 7963 over the next 30 days.

Let us increase the confidence level to 95% or the 2

standard deviation and check

what values we get –

Average + 2 SD (Upper Range) and Average – 2 SD (Lower Range)

= 1.15% + 2* 5.73% = 12.61%

= 1.15% – 2* 5.73% = -10.31%

Hence the range works out to –

= 8337 *exponential (12.61%)

= 9457 (Upper Range)

And for lower range –

= 8337 * exponential (-10.31%)

= 7520

I hope the above calculations are clear to you. You can also download the MS excel

that I’ve used to make these calculations.

Of course you may have a very valid point at this stage – normal distribution is fine,

but how do I get to use the information to trade? I guess as such this chapter is

quite long enough to accommodate more concepts. Hence we will move the

application part to the next chapter. In the next chapter we will explore the

applications of standard deviation (volatility) and its relevance to trading. We will

discuss two important topics in the next chapter (1) How to select strikes that can be

sold/written using normal distribution and (2) How to set up stoploss using volatility.

Of course, do remember eventually the idea is to discuss Vega and its effect on

options premium.

Key takeaways from this chapter

1. The daily returns of the stock is a random walk, highly difficult to predict

2. The returns of the stock is normally distributed or rather close to normal

distribution

3. In a normal distribution the data is centered around the mean and the dispersion is

measured by the standard deviation

4. Within 1 SD we can observe 68% of the data

5. Within 2 SD we can observe 95% of the data

6. Within 3 SD we can observe 99.5% of the data

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7. Events occurring outside the 3

standard deviation are referred to as Black Swan

events

8. Using the SD values we can calculate the upper and lower value of stocks/indices

167

Module 5 — Options Theory for Professional Trading

Chapter 18

Volatility Applications

251

18.1 – Striking it right

The last couple of chapters have given a basic understanding on volatility, standard

deviation, normal distribution etc. We will now use this information for few practical

trading applications. At this stage I would like to discuss two such applications –

1. Selecting the right strike to short/write

2. Calculating the stoploss for a trade

However at a much later stage (in a different module altogether) we will explore the

applications under a different topic – ‘Relative value Arbitrage (Pair Trading) and

Volatility Arbitrage’. For now we will stick to trading options and futures.

So let’s get started.

One of the key challenges an option writer always faces is to select the right strike

so that he can write that option, collect the premium, and not really be worried

about the possibility of the spot moving against him. Of course, the worry of spot

moving against the option writer will always exist, however a diligent trader can

minimize this.

Normal Distribution helps the trader minimize this worry and increase his

confidence while writing options.

Let’s have a quick recap –

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The bell curve above suggests that with reference to the mean (average) value –

1. 68% of the data is clustered around mean within the 1

SD, in other words there is a

68% chance that the data lies within the 1

2. 95% of the data is clustered around mean within the 2

SD, in other words there is a

95% chance that the data lies within the 2

3. 99.7% of the data is clustered around mean within the 3rd SD, in other words there

is a 99.7% chance that the data lies within the 3

Since we know that Nifty’s daily returns are normally distributed, the above set of

properties is applicable to Nifty. So what does it mean?

This means, if we know Nifty’s mean and SD then we can pretty much make an

‘educated guess’ about the range within which Nifty is likely to trade over the

selected time frame. Take this for example –

o Date = 11

August 2015

o Number of days for expiry = 16

o Nifty current market price = 8462

o Daily Average Return = 0.04%

o Annualized Return = 14.8%

o Daily SD = 0.89%

o Annualized SD = 17.04%

Given this I would now like to identify the range within which Nifty will trade until

expiry i.e 16 days from now –

16 day SD = Daily SD *SQRT (16)

= 0.89% * SQRT (16)

= 3.567%

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16 day average = Daily Avg * 16

= 0.04% * 16 = 0.65%

These numbers will help us calculate the upper and lower range within which Nifty

is likely to trade over the next 16 days –

Upper Range = 16 day Average + 16 day SD

= 0.65% + 3.567%

= 4.215%, to get the upper range number –

= 8462 * (1+4.215%)

= 8818

Lower Range = 16 day Average – 16 day SD

= 0.65% – 3.567%

= 2.920% to get the lower range number –

= 8462 * (1 – 2.920%)

= 8214

The calculation suggests that Nifty is likely to trade anywhere in the region of 8214

to 8818. How sure are we about this, well we know that there is a 68% probability

for this calculation to work in our favor. In other words there is 32% chance for Nifty

to trade outside 8214 and 8818 range. This also means all strikes outside the

calculated range ‘may’ go worthless.

Hence –

o You can sell all call options above 8818 and collect the premiums because they are

likely to expire worthless

o You can sell all put options below 8214 and collect the premiums because they are

likely to expire worthless

Alternatively if you were thinking of buying Call options above 8818 or Put options

below 8214 you may want to think twice, as you now know that there is a very little

chance for these options to expire in the money, hence it makes sense to avoid

buying these strikes.

Here is the snapshot of all Nifty Call option strikes above 8818 that you can choose

to write (short) and collect premiums –

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If I were to personally select a strike today it would be either 8850 or 8900 or

probably both and collect Rs.7.45 and Rs.4.85 in premium respectively. The reason

to select these strikes is simple – I see an acceptable balance between risk (1 SD

away) and reward (7.45 or 4.85 per lot).

I’m certain many of you may have this thought – if I were to write the 8850 Call

option and collect Rs.7.45 as premium, it does not really translate to any meaningful

amount. After all, at Rs.7.45 per lot it translates to –

= 7.45 * 25 (lot size)

= Rs.186.25

Well, this is exactly where many traders miss the plot. I know many who think about

the gains or loss in terms of absolute value and not really in terms of return on

investment.

Think about it, margin amount required to take this trade is roughly Rs.12,000/-. If

you are not sure about the margin requirement then I would suggest you use

Zerodha’s margin calculator.

The premium amount of Rs.186.25/- on a margin deposit of Rs.12,000/- works out to

a return of 1.55%, which by any stretch on imagination is not a bad return,

especially for a 16 day holding period! If you can consistently achieve this every

month, then we are talking about a return of over 18% annualized just by means of

option writing.

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I personally use this strategy to write options and I’d like to share some of my

thoughts regarding this –

Put Options – I don’t like to short PUT options for the simple reason that panic

spreads faster than greed. If there is panic in the market, the fall in market can be

much quicker than you can imagine. Hence even before you can realize the OTM

option that you have written can soon become ATM or ITM. Therefore it is better to

avoid than regret.

Call Options – You inverse the above point and you will understand why writing call

options are better than writing put options. For example in the Nifty example above,

for the 8900 CE to become ATM or ITM Nifty has to move 438 points over 16 days.

For this to happen, there has to be excess greed in the market…and like I said

earlier a 438 up move takes a bit longer than 438 down move. Therefore my

preference to short only call options.

Strike identification – I do the whole exercise of identifying the strike (SD, mean

calculation, converting the same w.r.t to number days to expiry, selecting

appropriate strike only the week before expiry and not before that. The timing here

is deliberate

Timing – I prefer to short options only on the last Friday before the expiry week. For

example given the August 2015 series expiry is on 27

, I’d short the call option only

on 21

August around the closing. Why do I do this? This is to mainly ensure that

theta works in my favor. Remember the ‘time decay’ graph we discussed in the theta

chapter? The graph makes it amply evident that theta kicks in full force as we

approach expiry.

Premium Collected – Because I write call options very close to expiry, the

premiums are invariably low. The premium that I collect is around Rs.5 or 6 on Nifty

Index, translating to about 1.0% return. But then I find the trade quite comforting

for two reasons – (1) For the trade to work against me Nifty has to move 1 SD over 4

days, something that does not happen frequently (2) Theta works in my favor, the

premiums erode much faster during the last week of expiry favoring the option

seller

Why bother ? – Most of you may have this thought that the premiums are so low,

why should I even bother? Honestly I too had this thought initially; however over

time I have realized that trades with the following characteristics makes sense to me

–

o Visibility on risk and reward – both should be quantifiable

o If a trade is profitable today then I should be able to replicate the same again

tomorrow

o Consistency in finding the opportunities

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o Assessment of worst case scenarios

This strategy ticks well on all counts above, hence my preference.

SD consideration – When I’m writing options 3-4 days before expiry I prefer to write

1 SD away, however for whatever reason when I’m writing the option much earlier

then I prefer to go 2 SD away. Remember higher the SD consideration, higher is the

confidence level but lower is the premium that you can collect. Also, as a thumb rule

I never write options when there is more than 15 days for expiry.

Events – I avoid writing options whenever there are important market events such

as monetary policy, policy decision, corporate announcement etc. This is because

the markets tend to react sharply to events and therefore a good chance of getting

caught on the wrong side. Hence it is better safe than sorry.

Black Swan – I’m completely aware that despite all the precaution, markets can

move against me and I could get caught on the wrong side. The price you pay for

getting caught on the wrong side, especially for this trade is huge. Imagine you

collect 5 or 6 points as premium but if you are caught on the wrong side you end up

paying 15 or 20 points or more. So all the small profits you made over 9 to 10

months is given away in 1 month. In fact the legendary Satyajit Das in his highly

insightful book “Traders, Guns, and Money” talks about option writing as “eating like

a hen but shitting like an elephant’.

The only way to make sure you minimize the impact of a black swan event is to be

completely aware that it can occur anytime after you write the option. So here is my

advice to you in case you decide to adopt this strategy – track the markets and

gauge the market sentiment all along. The moment you sense things are going

wrong be quick to exit the trade.

Success Ratio – Option writing keeps you on the edge of the seat. There are times

when you feel that markets are going against you (fear of black swan creeps in) but

only to cool off eventually. When you write options such roller coaster feelings are

bound to emerge. The worst part is that during this roller coaster ride you may be

forced to believe that the market is going against you (false signal) and hence you

get out of a potentially profitable trade.

In fact there is a very thin line between a false signal and an actual black swan

event. The way to overcome this is by developing conviction in your trades.

Unfortunately I cannot teach you conviction; you will have to develop that on your

own J. However your conviction improves as and when you do more of these trades

(and all trades should be backed by sound reasoning and not blind guesses).

Also, I personally get out of the trade when the option transitions from OTM to ATM.

Expenses – The key to these trades is to keep your expense to bear minimum so

that you can retain maximum profits for yourself. The expenses include brokerage

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and applicable charges. If you short 1 lot of Nifty options and collect Rs.7 as

premium then you will have to let go few points as expense. If you are trading with

Zerodha, your expense will be around 1.95 for 1 lot. The higher the number of lots

the lesser is your expense. So if I were trading 10 lots (with Zerodha) instead of 1,

my expense drastically comes down to 0.3 points. You can use Zerodha’s brokerage

calculator to get the details.

The cost varies broker to broker so please do make sure your broker is not greedy

by charging you ridiculous brokerage fees. Even better, if you are not with Zerodha,

it is about time you join us and become a part of our beautiful family

Capital Allocation – An obvious question you might have at this stage – how much

money do I deploy to this trade? Do I risk all my capital or only a certain %? If it’s a %,

then how much would it be? There is no straight forward answer to this; hence I’ll

take this opportunity to share my asset allocation technique.

I’m a complete believer in equities as an asset class, so this rules out investment in

Gold, Fixed Deposit, and Real Estate for me. 100% of my capital (savings) is invested

in equity and equity based products. However it is advisable for any individual to

diversify capital across multiple asset classes.

So within Equity, here is how I split my money –

o 35% of my money is invested in equity based mutual funds via SIP (systematic

investment plan) route. I have further divided this across 4 funds.

o 40% of my capital in an equity portfolio of about 12 stocks. I consider both mutual

funds and equity portfolio as long term investments (5 years and beyond).

o 25% is earmarked for short term strategies.

The short term strategies include a bunch of trading strategies such as –

o Momentum based swing trades (futures)

o Overnight futures/options/stock trades

o Intraday trades

o Option writing

I make sure that I do not expose more than 35% of the 25% capital for any particular

strategy. Just to make it more clear, assume I have Rs.500,000/- as my capital, here

is how I would split my money –

o 35% of Rs.500,000/- i.e Rs.175,000/- goes to Mutual Funds

o 40% of Rs.500,000/- i.e Rs.200,000/- goes to equity portfolio

o 25% of Rs.500,000/- i.e Rs.125,000/- goes to short term trading

o 35% of Rs.125,000/- i.e Rs.43,750/- is the maximum I would allocate per trade

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o Hence I will not short more than 4 lots of options

o 43,750/- is about 8.75% of the overall capital of Rs.500,000/-

So this self mandated rule ensures that I do not expose more than 9% of my over all

capital to any particular short term strategies including option writing.

Instruments – I prefer running this strategy on liquid stocks and indices. Besides

Nifty and Bank Nifty I run this strategy on SBI, Infosys, Reliance, Tata Steel, Tata

Motors, and TCS. I rarely venture outside this list.

So here is what I would suggest you do. Run the exercise of calculating the SD and

mean for Nifty, Bank Nifty on the morning of August 21

(5 to 7 days before expiry).

Identify strikes that are 1 SD away from the market price and write them virtually.

Wait till the expiry and experience how this trade goes. If you have the bandwidth

you can run this across all the stocks that I’ve mentioned. Do this diligently for few

expiries before you can deploy capital.

Lastly, as a standard disclaimer I have to mention this – the thoughts expressed

above suits my risk reward temperament, which could be very different from yours.

Everything that I mentioned here comes from my own personal trading experience,

these are not standard practices.

I would suggest you note these points, understand your own risk-reward

temperament, and calibrate your strategy. Hopefully the pointers here should help

you develop that orientation.

This is quite contradicting to this chapter but I have to recommend you to read

Nassim Nicholas Taleb’s “Fooled by Randomness” at this point. The book makes you

question and rethink everything that you do in markets (and life in general). I think

just being completely aware of what Taleb writes in his book along with the actions

you take in markets puts you in a completely different orbit.

18.2 – Volatility based stoploss

The discussion here is a digression from Options, in fact this would have been more

apt in the futures trading module, but I think we are at the right stage to discuss this

topic.

The first thing you need to identify before you initiate any trade is to identify the

stop-loss (SL) price for the trade. As you know, the SL is a price point beyond which

you will not take any further losses. For example, if you buy Nifty futures at 8300,

you may identify 8200 as your stop-loss level; you will be risking 100 points on this

particular trade. The moment Nifty falls below 8200, you exit the trade taking the

loss. The question however is – how to identify the appropriate stop-loss level?

One standard approach used by many traders is to keep a standard pre-fixed

percentage stop-loss. For example one could have a 2% stop-loss on every trade. So

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if you are to buy a stock at Rs.500, then your stop-loss price is Rs.490 and you risk

Rs.10 (2% of Rs.500) on this trade. The problem with this approach lies in the rigidity

of the practice. It does not account for the daily noise / volatility of the stock. For

example the nature of the stock could be such that it could swing about 2-3% on a

daily basis. As a result you could be right about the direction of the trade but could

still hit a ‘stop-loss’. More often than not, you would regret keeping such tight stops.

An alternate and effective method to identify a stop-loss price is by estimating the

stock’s volatility. Volatility accounts for the daily ‘expected’ fluctuation in the stock

price. The advantage with this approach is that the daily noise of the stock is

factored in. Volatility stop is strategic as it allows us to place a stop at the price

point which is outside the normal expected volatility of the stock. Therefore a

volatility SL gives us the required logical exit in case the trade goes against us.

Let’s understand the implementation of the volatility based SL with an example.

This is the chart of Airtel forming a bullish harami, people familiar with the pattern

would immediately recognize this is an opportunity to go long on the stock, keeping

the low of the previous day (also coinciding with a support) as the stoploss. The

target would be the immediate resistance – both S&R points are marked with a blue

line. Assume you expect the trade to materialize over the next 5 trading sessions.

The trade details are as follows –

o Long @ 395

o Stop-loss @ 385

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o Target @ 417

o Risk = 395 – 385 = 10 or about 2.5% below entry price

o Reward = 417 – 385 = 32 or about 8.1% above entry price

o Reward to Risk Ratio = 32/10 = 3.2 meaning for every 1 point risk, the expected

reward is 3.2 point

This sounds like a good trade from a risk to reward perspective. In fact I personally

consider any short term trade that has a Reward to Risk Ratio of 1.5 as a good trade.

However everything hinges upon the fact that the stoploss of 385 is sensible.

Let us make some calculations and dig a little deeper to figure out if this makes

sense –

Step 1: Estimate the daily volatility of Airtel. I’ve done the math and the daily

volatility works out to 1.8%

Step 2: Convert the daily volatility into the volatility of the time period we are

interested in. To do this, we multiply the daily volatility by the square root of time. In

our example, our expected holding period is 5 days, hence the 5 day volatility is

equal to 1.8%*Sqrt(5). This works out to be about 4.01%.

Step 3. Calculate the stop-loss price by subtracting 4.01% (5 day volatility) from the

expected entry price. 395 – (4.01% of 395) = 379. The calculation above indicates

that Airtel can swing from 395 to 379 very easily over the next 5 days. This also

means, a stoploss of 385 can be easily knocked down. So the SL for this trade has be

a price point below 379, lets say 375, which is 20 points below the entry price of 395.

Step 4 : With the new SL, the RRR works out to 1.6 (32/20), which still seems ok to

me. Hence I would be happy to initiate the trade.

Note : In case our expected holding period is 10 days, then the 10 day volatility

would be 1.6*sqrt(10) so on and so forth.

Pre-fixed percentage stop-loss does not factor in the daily fluctuation of the stock

prices. There is a very good chance that the trader places a premature stop-loss,

well within the noise levels of the stock. This invariably leads to triggering the stop-

loss first and then the target.

Volatility based stop-loss takes into account all the daily expected fluctuation in the

stock prices. Hence if we use a stocks volatility to place our stop-loss, then we would

be factoring in the noise component and in turn placing a more relevant stop loss.

Key takeaways from this chapter

o You can use SD to identify strikes that you can write

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o Avoid shorting PUT options

o Strikes 1 SD away offers 68% flexibility, if you need higher flexibility you could opt

for 2SD

o Higher the SD, higher is the range, and lower is the premium collected

o Allocate capital based on your belief in asset classes. It is always advisable to invest

across asset classes

o It always makes sense to place SL based on daily volatility of the stock

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Module 5 — Options Theory for Professional Trading

Chapter 19

Vega

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19.1 – Volatility Types

The last few chapters have laid a foundation of sorts to help us understand Volatility

better. We now know what it means, how to calculate the same, and use the

volatility information for building trading strategies. It is now time to steer back to

the main topic – Option Greek and in particular the 4

Option Greek “Vega”. Before

we start digging deeper into Vega, we have to discuss one important topic – Quentin

Tarantino .

I’m huge fan of Quentin Tarantino and his movies. For people not familiar with

Quentin Tarantino let me tell you, he is one of the most talented directors in

Hollywood. He is the man behind super cult flicks such as Pulp Fiction, Kill Bill,

Reservoir Dogs, Django Unchained etc. If you’ve not watched his movies, I’d suggest

you do, you may just love these movies as much as I do.

It is a known fact that when Quentin Tarantino directs a movie, he keeps all the

production details under wraps until the movies trailer hits the market. Only after

the trailer is out people get to know the name of movie, star cast details, brief story

line, movie location etc. However, this is not the case with the movie he is directing

these days, titled “The Hateful Eight”, due to be released in December 2015.

Somehow everything about ‘The Hateful Eight’ – the star cast, storyline, location etc

is leaked, hence people already know what to expect from Tarantino. Now given

that most of the information about the movie is already known, there are wild

speculations about the box office success of his upcoming movie.

We could do some analysis on this –

1. Past movies – We know almost all of Tarantino’s previous movies were successful.

Based on his past directorial performance we can be reasonably certain that ‘The

Hateful Eight’ is likely to be a box office hit

2. Movie Analyst’s forecast – There are these professional Hollywood movie analysts,

who understand the business of cinema very well. Some of these analysts are

forecasting that ‘The Hateful Eight’ may not do well (unlike his previous flicks) as

most of the details pertaining to the movie is already, failing to enthuse the

audience

3. Social Media – If you look at the discussions on ‘The Hateful Eight’ on social media

sites such as Twitter and Facebook, you’d realize that a lot of people are indeed

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excited about the movie, despite knowing what to expect from the movie. Going by

the reactions on Social Media, ‘The Hateful Eight’ is likely to be a hit.

4. The actual outcome – Irrespective of what really is being expected, once the movie

is released we would know if the movie is a hit or a flop. Of course this is the final

verdict for which we have to wait till the movie is released.

Tracking the eventual fate of the movie is not really our concern, although I’m

certainly going to watch the movie .

Given this, you may be wondering why we are even discussing Quentin Tarantino in

a chapter concerning Options and Volatility! Well this is just my attempt (hopefully

not lame) to explain the different types of volatility that exist – Historical Volatility,

Forecasted Volatility, and Implied Volatility. So let’s get going.

Historical Volatility is similar to us judging the box office success of ‘The Hateful

Eight’ based on Tarantino’s past directorial ventures. In the stock market world, we

take the past closing prices of the stock/index and calculate the historical volatility.

Do recall, we discussed the technique of calculating the historical volatility in

Chapter 16. Historical volatility is very easy to calculate and helps us with most of

the day to day requirements – for instance historical volatility can ‘somewhat’ be

used in the options calculator to get a ‘quick and dirty’ option price (more on this in

the subsequent chapters).

Forecasted Volatility is similar to the movie analyst attempting to forecast the fate

of ‘The Hateful Eight’. In the stock market world, analysts forecast the volatility.

Forecasting the volatility refers to the act of predicting the volatility over the desired

time frame.

However, why would you need to predict the volatility? Well, there are many option

strategies, the profitability of which solely depends on your expectation of volatility.

If you have a view of volatility – for example you expect volatility to increase by

12.34% over the next 7 trading sessions, then you can set up option strategies which

can profit this view, provided the view is right.

Also, at this stage you should realize – to make money in the stock markets it is NOT

necessary to have a view on the direction on the markets. The view can be on

volatility as well. Most of the professional options traders trade based on volatility

and not really the market direction. I have to mention this – many traders find

forecasting volatility is far more efficient than forecasting market direction.

Now clearly having a mathematical/statistical model to predict volatility is much

better than arbitrarily declaring “I think the volatility is going to shoot up”. There are

a few good statistical models such as ‘Generalized AutoRegressive Conditional

Heteroskedasticity (GARCH) Process’. I know it sounds spooky, but that’s what it’s

called. There are several GARCH processes to forecast volatility, if you are venturing

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into this arena, I can straightaway tell you that GARCH (1,1) or GARCH (1,2) are

better suited processes for forecasting volatility.

Implied Volatility (IV) is like the people’s perception on social media. It does not

matter what the historical data suggests or what the movie analyst is forecasting

about ‘The Hateful Eight’. People seem to be excited about the movie, and that is an

indicator of how the movie is likely to fare. Likewise the implied volatility represents

the market participant’s expectation on volatility. So on one hand we have the

historical and forecasted volatility, both of which are sort of ‘manufactured’ while on

the other hand we have implied volatility which is in a sense ‘consensual’. Implied

volatility can be thought of as consensus volatility arrived amongst all the market

participants with respect to the expected amount of underlying price fluctuation

over the remaining life of an option. Implied volatility is reflected in the price of the

premium.

For this reason amongst the three different types of volatility, the IV is usually more

valued.

You may have heard or noticed India VIX on NSE website, India VIX is the official

‘Implied Volatility’ index that one can track. India VIX is computed based on a

mathematical formula, here is a whitepaper which explains how India VIX is

calculated –

If you find the computation a bit overwhelming, then here is a quick wrap on what

you need to know about India VIX (I have reproduced some of these points from the

NSE’s whitepaper) –

1. NSE computes India VIX based on the order book of Nifty Options

2. The best bid-ask rates for near month and next-month Nifty options contracts are

used for computation of India VIX

3. India VIX indicates the investor’s perception of the market’s volatility in the near

term (next 30 calendar days)

4. Higher the India VIX values, higher the expected volatility and vice-versa

5. When the markets are highly volatile, market tends to move steeply and during such

time the volatility index tends to rise

6. Volatility index declines when the markets become less volatile. Volatility indices

such as India VIX are sometimes also referred to as the ‘Fear Index’, because as the

volatility index rises, one should become careful, as the markets can move steeply

into any direction. Investors use volatility indices to gauge the market volatility and

make their investment decisions

7. Volatility Index is different from a market index like NIFTY. NIFTY measures the

direction of the market and is computed using the price movement of the

underlying stocks whereas India VIX measures the expected volatility and is

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computed using the order book of the underlying NIFTY options. While Nifty is a

number, India VIX is denoted as an annualized percentage

Further, NSE publishes the implied volatility for various strike prices for all the

options that get traded. You can track these implied volatilities by checking the

option chain. For example here is the option chain of Cipla, with all the IV’s marked

out.

The Implied Volatilities can be calculated using a standard options calculator. We

will discuss more about calculating IV, and using IV for setting up trades in the

subsequent chapters. For now we will now move over to understand Vega.

Realized Volatility is pretty much similar to the eventual outcome of the movie,

which we would get to know only after the movie is released. Likewise the realized

volatility is looking back in time and figuring out the actual volatility that occurred

during the expiry series. Realized volatility matters especially if you want to compare

today’s implied volatility with respect to the historical implied volatility. We will

explore this angle in detail when we take up “Option Trading Strategies”.

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19.2 – Vega

Have you noticed this – whenever there are heavy winds and thunderstorms, the

electrical voltage in your house starts fluctuating violently, and with the increase in

voltage fluctuations, there is a chance of a voltage surge and therefore the

electronic equipments at house may get damaged.

Similarly, when volatility increases, the stock/index price starts swinging heavily. To

put this in perspective, imagine a stock is trading at Rs.100, with increase in

volatility, the stock can start moving anywhere between 90 and 110. So when the

stock hits 90, all PUT option writers start sweating as the Put options now stand a

good chance of expiring in the money. Similarly, when the stock hits 110, all CALL

option writers would start panicking as all the Call options now stand a good chance

of expiring in the money.

Therefore irrespective of Calls or Puts when volatility increases, the option

premiums have a higher chance to expire in the money. Now, think about this –

imagine you want to write 500 CE options when the spot is trading at 475 and 10

days to expire. Clearly there is no intrinsic value but there is some time value. Hence

assume the option is trading at Rs.20. Would you mind writing the option? You may

write the options and pocket the premium of Rs.20/- I suppose. However, what if the

volatility over the 10 day period is likely to increase – maybe election results or

corporate results are scheduled at the same time. Will you still go ahead and write

the option for Rs.20? Maybe not, as you know with the increase in volatility, the

option can easily expire ‘in the money’ hence you may lose all the premium money

you have collected. If all option writers start fearing the volatility, then what would

compel them to write options? Clearly, a higher premium amount would. Therefore

instead of Rs.20, if the premium was 30 or 40, you may just think about writing the

option I suppose.

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In fact this is exactly what goes on when volatility increases (or is expected to

increase) – option writers start fearing that they could be caught writing options that

can potentially transition to ‘in the money’. But nonetheless, fear too can be

overcome for a price, hence option writers expect higher premiums for writing

options, and therefore the premiums of call and put options go up when volatility is

expected to increase.

The graphs below emphasize the same point –

X axis represents Volatility (in %) and Y axis represents the premium value in

Rupees. Clearly, as we can see, when the volatility increases, the premiums also

increase. This holds true for both call and put options. The graphs here go a bit

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further, it shows you the behavior of option premium with respect to change in

volatility and the number of days to expiry.

Have a look at the first chart (CE), the blue line represents the change in premium

with respect to change in volatility when there is 30 days left for expiry, likewise the

green and red line represents the change in premium with respect to change in

volatility when there is 15 days left and 5 days left for expiry respectively.

Keeping this in perspective, here are a few observations (observations are common

for both Call and Put options) –

1. Referring to the Blue line – when there are 30 days left for expiry (start of the series)

and the volatility increases from 15% to 30%, the premium increases from 97 to 190,

representing about 95.5% change in premium

2. Referring to the Green line – when there are 15 days left for expiry (mid series) and

the volatility increases from 15% to 30%, the premium increases from 67 to 100,

representing about 50% change in premium

3. Referring to the Red line – when there are 5 days left for expiry (towards the end of

series) and the volatility increases from 15% to 30%, the premium increases from 38

to 56, representing about 47% change in premium

Keeping the above observations in perspective, we can make few deductions –

1. The graphs above considers a 100% increase of volatility from 15% to 30% and its

effect on the premiums. The idea is to capture and understand the behavior of

increase in volatility with respect to premium and time. Please be aware that

observations hold true even if the volatility moves by smaller amounts like maybe

20% or 30%, its just that the respective move in the premium will be proportional

2. The effect of Increase in volatility is maximum when there are more days to expiry –

this means if you are at the start of series, and the volatility is high then you know

premiums are plum. Maybe a good idea to write these options and collect the

premiums – invariably when volatility cools off, the premiums also cool off and you

could pocket the differential in premium

3. When there are few days to expiry and the volatility shoots up the premiums also

goes up, but not as much as it would when there are more days left for expiry. So if

you are a wondering why your long options are not working favorably in a highly

volatile environment, make sure you look at the time to expiry

So at this point one thing is clear – with increase in volatility, the premiums increase,

but the question is ‘by how much?’. This is exactly what the Vega tells us.

The Vega of an option measures the rate of change of option’s value (premium) with

every percentage change in volatility. Since options gain value with increase in

volatility, the vega is a positive number, for both calls and puts. For example – if the

option has a vega of 0.15, then for each % change in volatility, the option will gain or

lose 0.15 in its theoretical value.

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19.3 – Taking things forward

It is now perhaps time to revisit the path this module on Option Trading has taken

and will take going forward (over the next few chapters).

We started with the basic understanding of the options structure and then

proceeded to understand the Call and Put options from both the buyer and sellers

perspective. We then moved forward to understand the moneyness of options and

few basic technicalities with respect to options.

We further understood option Greeks such as the Delta, Gamma, Theta, and Vega

along with a mini series of Normal Distribution and Volatility.

At this stage, our understanding on Greeks is one dimensional. For example we

know that as and when the market moves the option premiums move owing to

delta. But in reality, there are several factors that works simultaneously – on one

hand we can have the markets moving heavily, at the same time volatility could be

going crazy, liquidity of the options getting sucked in and out, and all of this while

the clock keeps ticking. In fact this is exactly what happens on an everyday basis in

markets. This can be a bit overwhelming for newbie traders. It can be so

overwhelming that they quickly rebrand the markets as ‘Casino’. So the next time

you hear someone say such a thing about the markets, make sure you point them

to Varsity .

Anyway, the point that I wanted to make is that all these Greeks manifest itself on

the premiums and therefore the premiums vary on a second by second basis. So it

becomes extremely important for the trader to fully understand these ‘inter Greek’

interactions of sorts. This is exactly what we will do in the next chapter. We will also

have a basic understanding of the Black & Scholes options pricing formula and how

to use the same.

19.4 – Flavors of Inter Greek Interactions

(The following article was featured in Business Line dated 31st August 2015)

Here is something that happened very recently. By now everyone remotely

connected with the stock market would know that on 24

August 2015, the Indian

markets declined close to 5.92% making it one of the worse single day declines in

the history of Indian stock markets. None of the front line stocks survived the

onslaught and they all declined by 8-10%. Panic days such as these are a common

occurrence in the equity markets.

However something unusual happened in the options markets on 24

August 2015,

here are some data points from that day –

Nifty declined by 4.92% or about 490 points –

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India VIX shot up by 64% –

But Call option Premiums shot up!

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Traders familiar with options would know that the call option premiums decline

when market declines. In fact most of the call option premiums (strikes below 8600)

did decline in value but option strikes above 8650 behaved differently – their

premium as opposed to the general expectation did not decline, rather increased by

50-80%. This move has perplexed many traders, with many of the traders

attributing this move to random theories such as rate rigging, market manipulation,

technological inefficiency, liquidity issues etc. But I suspect any of this is true; in fact

this can be explained based on the option theory logic.

We know that option premiums are influenced by sensitivity factors aka the Option

Greeks. Delta as we know captures the sensitivity of options premium with respect

to the movement of the underlying. Here is a quick recap – if the Delta of a

particular call option is 0.75, then for every 1 point increase/decrease in the

underlying the premium is expected to increase/decrease by 0.75 points. On

August, Nifty declined by 490 points, so all call options which had ‘noticeable

Delta’ (like 0.2, 0.3, 0.6 etc) declined. Typically ‘in the money’ options (as on 24

Aug,

all strike below 8600) tend to have noticeable Delta, therefore all their premiums

declined with the decline in the underlying.

‘Out of the money’ options usually have a very low delta like 0.1 or lower. This

means, irrespective of the move in the underlying the moment in the option

premium will be very restrictive. As on August 24

, all options above 8600 were ‘out

of the money’ options with low delta values. Hence irrespective of the massive fall in

the market, these call options did not lose much premium value.

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The above explains why certain call options did not lose value, but why did the

premiums go up? The answer to this is lies in Vega – the option Greek which

captures the sensitivity of market volatility on options premiums.

With increase in volatility, the Vega of an option increases (irrespective of calls and

puts), and with increase in Vega, the option premium tends to increase. On

August the volatility of Indian markets shot up by 64%. This increase in volatility

was totally unexpected by the market participants. With the increase in volatility, the

Vega of all options increases, thereby their respective premiums also increased. The

effect of Vega is particularly high for ‘Out of the money’ options. So on one hand the

low delta value of ‘out of the money’ call options prevented the option premiums

from declining while on the other hand, high Vega value increased the option

premium for these out of the money options.

Hence on 24

August 2015 we got to witness the unusual – call option premium

increasing 50 – 80% on a day when markets crashed 5.92%.

Key takeaways from this chapter

1. Historical Volatility is measured by the closing prices of the stock/index

2. Forecasted Volatility is forecasted by volatility forecasting models

3. Implied Volatility represents the market participants expectation of volatility

4. India VIX represents the implied volatility over the next 30 days period

5. Vega measures the rate of change of premium with respect to change in volatility

6. All options increase in premium when volatility increases

7. The effect of volatility is highest when there are more days left for expiry

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Module 5 — Options Theory for Professional Trading

Chapter 20

Greek Interactions

178

20.1 – Volatility Smile

We had briefly looked at inter Greek interactions in the previous chapter and how

they manifest themselves on the options premium. This is an area we need to

explore in more detail, as it will help us select the right strikes to trade. However

before we do that we will touch upon two topics related to volatility called ‘Volatility

Smile’ and ‘Volatility Cone’.

Volatility Smile is an interesting concept, something that I consider ‘good to know’

kind of concept. For this reason I will just touch upon this and not really dig deeper

into it.

Theoretically speaking, all options of the same underlying, expiring on the same

expiry day should display similar ‘Implied Volatilities’ (IV). However in reality this

does not happen.

Have a look at this image –

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This is the option chain of SBI as of 4

September 2015. SBI is trading around 225,

hence the 225 strike becomes ‘At the money’ option, and the same is highlighted

with a blue band. The two green bands highlight the implied volatilities of all the

other strikes. Notice this – as you go away from the ATM option (for both Calls and

Puts) the implied volatilities increase, in fact further you move from ATM, the higher

is the IV. You can notice this pattern across all the different stocks/indices. Further

you will also observe that the implied volatility of the ATM option is the lowest. If

you plot a graph of all the options strikes versus their respective implied volatility

you will get to see a graph similar to the one below –

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The graph appears like a pleasing smile; hence the name ‘Volatility Smile’

20.2 – Volatility Cone

(All the graphs in this chapter and in this section on Volatility Cone has been authored

by Prakash Lekkala)

So far we have not touched upon an option strategy called ‘Bull Call Spread’, but for

the sake of this discussion I will make an assumption that you are familiar with this

strategy.

For an options trader, implied volatility of the options greatly affects the

profitability. Consider this – you are bullish on stock and want to initiate an option

strategy such as a Bull Call Spread. If you initiate the trade when the implied

volatility of options is high, then you will have to incur high upfront costs and lower

profitability potential. However if you initiate the position when the option implied

volatility is low, your trading position will incur lower costs and higher potential

profit.

For instance as of today, Nifty is trading at 7789. Suppose the current implied

volatility of option positions is 20%, then a 7800 CE and 8000 CE bull call spread

would cost 72 with a potential profit of 128. However if the implied volatility is 35%

instead of 20%, the same position would cost 82 with potential profit of 118. Notice

with higher volatility a bull call spread not only costs higher but the profitability

greatly reduces.

So the point is for option traders , it becomes extremely crucial to assess the level of

volatility in order to time the trade accordingly. Another problem an option trader

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has to deal with is, the selection of the underlying and the strike (particularly true if

your strategies are volatility based).

For example – Nifty ATM options currently have an IV of ~25%, whereas SBI ATM

options have an IV of ~52%, given this should you choose to trade Nifty options

because IV is low or should you go with SBI options?

This is where the Volatility cone comes handy – it addresses these sorts of questions

for Option traders. Volatility Cone helps the trader to evaluate the costliness of an

option i.e. identify options which are trading costly/cheap. The good news is, you

can do it not only across different strikes of a security but also across different

securities as well.

Let’s figure out how to use the Volatility Cone.

Below is a Nifty chart for the last 15 months. The vertical lines mark the expiry dates

of the derivative contracts, and the boxes prior to the vertical lines mark the price

movement of Nifty 10 days prior to expiry.

If you calculate the Nifty’s realized volatility in each of the boxes, you will get the

following table –

Expiry Date

Annualized realized volatility

Jun-14

41%

Jul-14

38%

Aug-14

33%

Sep-14

28%

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Oct-14

28%

Nov-14

41%

Dec-14

26%

Jan-15

22%

Feb-15

56%

Mar-15

19%

Apr-15

13%

May-15

34%

Jun-15

17%

Jul-15

41%

Aug-15

21%

From the above table we can observe that Nifty’s realized volatility has ranged from

a maximum of 56% (Feb 2015) to a minimum of 13% (April 2015).

We can also calculate mean and variance of the realized volatility, as shown below –

Particulars

Details

Maximum Volatility

56%

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+2 Standard Deviation (SD)

54%

+1 Standard Deviation (SD)

42%

Mean/ Average Volatility

31%

-1 Standard Deviation (SD)

19%

-2 Standard Deviation (SD)

Minimum Volatility

13%

If we repeat this exercise for 10, 20, 30, 45, 60 & 90 day windows, we would get a

table as follows –

Days to Expiry

Max

56%

49%

41%

40%

37%

35%

+2 SD

54%

46%

42%

41%

40%

38%

+1 SD

42%

38%

36%

35%

33%

Mean/Average

30%

29%

30%

29%

-1 SD

19%

21%

23%

24%

-2 SD

13%

17%

19%

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Min

13%

16%

21%

22%

21%

20%

The graphical representation of the table above would look like a cone as shown

below, hence the name ‘Volatility Cone’ –

The way to read the graph would be to first identify the ‘Number of days to Expiry’

and then look at all the data points that are plotted right above it. For example if the

number of days to expiry is 30, then observe the data points (representing realized

volatility) right above it to figure out the ‘Minimum, -2SD, -1 SD, Average implied

volatility etc’. Also, do bear in mind; the ‘Volatility Cone’ is a graphical representation

on the ‘historical realized volatility’.

Now that we have built the volatility cone, we can plot the current day’s implied

volatility on it. The graph below shows the plot of Nifty’s near month (September

2015) and next month (October 2015) implied volatility on the volatility cone.

Each dot represents the implied volatility for an option contract – blue are for call

options and black for put options.

For example starting from left, look at the first set of dots – there are 3 blue and

black dots. Each dot represents an implied volatility of an option contract – so the

first blue dot from bottom could be the implied volatility of 7800 CE, above that it

could be the implied volatility of 8000 CE and above that it could be the implied

volatility of 8100 PE etc.

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Do note the first set of dots (starting form left) represent near month options

(September 2015) and are plotted at 12 on x-axis, i.e. these options will expire 12

days from today. The next set of dots is for middle month (October 2015) plotted at

43, i.e. these options will expire 43 days from today.

Interpretation

Look at the 2nd set of dots from left. We can notice a blue dot above the +2SD line

(top most line, colored in maroon) for middle month option. Suppose this dot is for

option 8200 CE, expiring 29-Oct-2015, then it means that today 8200 CE is

experiencing an implied volatility, which is higher (by +2SD) than the volatility

experienced in this stock whenever there are “43 days to expiry” over the last 15

months [remember we have considered data for 15 months]. Therefore this option

has a high IV, hence the premiums would be high and one can consider designing a

trade to short the ‘volatility’ with an expectation that the volatility will cool off.

Similarly a black dot near -2 SD line on the graph, is for a Put option. It suggests that,

this particular put option has very low IV, hence low premium and therefore it could

be trading cheap. One can consider designing a trade so as to buy this put option.

A trader can plot volatility cone for stocks and overlap it with the option’s current IV.

In a sense, the volatility cone helps us develop an insight about the state of current

implied volatility with respect to the past realized volatility.

Those options which are close to + 2SD line are trading costly and options near -2

SD line are considered to be trading cheap. Trader can design trades to take

advantage of ‘mispriced’ IV. In general, try to short options which are costlier and go

long on options which are trading cheap.

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Please note: Use the plot only for options which are liquid.

With this discussion on Volatility Smile and Volatility Cone, hopefully our

understanding on Volatility has come to a solid ground.

20.3 – Gamma vs Time

Over the next two sections let us focus our attention to inter greek interactions.

Let us now focus a bit on greek interactions, and to begin with we will look into the

behavior of Gamma with respect to time. Here are a few points that will help refresh

your memory on Gamma –

o Gamma measures the rate of change of delta

o Gamma is always a positive number for both Calls and Puts

o Large Gamma can translate to large gamma risk (directional risk)

o When you buy options (Calls or Puts) you are long Gamma

o When you short options (Calls or Puts) you are short Gamma

o Avoid shorting options which have a large gamma

The last point says – avoid shorting options which have a large gamma. Fair enough,

however imagine this – you are at a stage where you plan to short an option which

has a small gamma value. The idea being you short the low gamma option and hold

the position till expiry so that you get to keep the entire option premium. The

question however is, how do we ensure the gamma is likely to remain low

throughout the life of the trade?

The answer to this lies in understanding the behavior of Gamma versus time to

expiry/maturity. Have a look at the graph below –

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The graph above shows how the gamma of ITM, ATM, and OTM options behave as

the ‘time to expiry’ starts to reduce. The Y axis represents gamma and the X axis

represents time to expiry. However unlike other graphs, don’t look at the X – axis

from left to right, instead look at the X axis from right to left. At extreme right, the

value reads 1, which suggests that there is ample time to expiry. The value at the left

end reads 0, meaning there is no time to expiry. The time lapse between 1 and 0 can

be thought of as any time period – 30 days to expiry, 60 days to expiry, or 365 days

to expiry. Irrespective of the time to expiry, the behavior of gamma remains the

same.

The graph above drives across these points –

o When there is ample time to expiry, all three options ITM, ATM, OTM have low

Gamma values. ITM option’s Gamma tends to be lower compared to ATM or OTM

options

o The gamma values for all three strikes (ATM, OTM, ITM) remain fairly constant till

they are half way through the expiry

o ITM and OTM options race towards zero gamma as we approach expiry

o The gamma value of ATM options shoot up drastically as we approach expiry

From these points it is quite clear that, you really do not want to be shorting “ATM”

options, especially close to expiry as ATM Gamma tends to be very high.

In fact if you realize we are simultaneously talking about 3 variables here – Gamma,

Time to expiry, and Option strike. Hence visualizing the change in one variable with

respect to change in another makes sense. Have a look at the image below –

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The graph above is called a ‘Surface Plot’, this is quite useful to observe the behavior

of 3 or more variables. The X-axis contains ‘Time to Expiry’ and the ‘Y axis’ contains

the gamma value. There is another axis which contains ‘Strike’.

There are a few red arrows plotted on the surface plot. These arrows are placed to

indicate that each line that the arrow is pointing to, refers to different strikes. The

outermost line (on either side) indicates OTM and ITM strikes, and the line at the

center corresponds to ATM option. From these lines it is very clear that as we

approach expiry, the gamma values of all strikes except ATM tends to move towards

zero. The ATM and few strikes around ATM have non zero gamma values. In fact

Gamma is highest for the line at the center – which represents ATM option.

We can look at it from the perspective of the strike price –

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This is the same graph but shown from a different angle, keeping the strike in

perspective. As we can see, the gamma of ATM options shoot up while the Gamma

of other option strikes don’t.

In fact here is a 3D rendering of Gamma versus Strike versus Time to Expiry. The

graph below is a GIF, in case it refuses to render properly, please do click on it to see

it in action.

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Hopefully the animated version of the surface plot gives you a sense of how gamma,

strikes, and time to expiry behave in tandem.

20.4 – Delta versus implied volatility

These are interesting times for options traders, have a look at the image below –

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The snapshot was taken on 11

September when Nifty was trading at 7,794. The

snapshot is that of 6800 PE which is currently trading at Rs.8.3/-.

Figure this, 6800 is a good 1100 points way from the current Nifty level of 7794. The

fact that 6800 PE is trading at 5.5 implies there are a bunch of traders who expect

the market to move 1100 points lower within 11 trading sessions (do note there are

also 2 trading holidays from now to expiry).

Given the odds of Nifty moving 1100 (14% lower from present level) in 11 trading

sessions are low, why is the 6800 PE trading at 8.3? Is there something else driving

the options prices higher besides pure expectations? Well, the following graph may

just have the answer for you –

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The graph represents the movement of Delta with respect to strike price. Here is

what you need to know about the graph above –

o The blue line represents the delta of a call option, when the implied volatility is 20%

o The red line represents the delta of a call option, when the implied volatility is 40%

o The green line represents the delta of a Put option, when the implied volatility is

20%

o The purple line represents the delta of a Put option, when the implied volatility is

40%

o The call option Delta varies from 0 to 1

o The Put option Delta varies from 0 to -1

o Assume the current stock price is 175, hence 175 becomes ATM option

With the above points in mind, let us now understand how these deltas behave –

o Starting from left – observe the blue line (CE delta when IV is 20%), considering 175

is the ATM option, strikes such as 135, 145 etc are all Deep ITM. Clearly Deep ITM

options have a delta of 1

o When IV is low (20%), the delta gets flattened at the ends (deep OTM and ITM

options). This implies that the rate at which Delta moves (further implying the rate

at which the option premium moves) is low. In other words deep ITM options tends

to behave exactly like a futures contract (when volatility is low) and OTM option

prices will be close to zero.

o You can observe similar behavior for Put option with low volatility (observe the

green line)

o Look at the red line (delta of CE when volatility is 40%) – we can notice that the end

(ITM/OTM) is not flattened, in fact the line appears to be more reactive to underlying

price movement. In other words, the rate at which the option’s premium change

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with respect to change in underlying is high, when volatility is high. In other words, a

large range of options around ATM are sensitive to spot price changes, when

volatility is high.

o Similar observation can be made for the Put options when volatility is high (purple

line)

o Interestingly when the volatility is low (look at the blue and green line) the delta of

OTM options goes to almost zero. However when the volatility is high, the delta of

OTM never really goes to zero and it maintains a small non zero value.

Now, going back to the initial thought – why is the 6800 PE, which is 1100 points

away trading at Rs.8.3/-?

Well that’s because 6800 PE is a deep OTM option, and as the delta graph above

suggests, when the volatility is high (see image below), deep OTM options have non

zero delta value.

I would suggest you draw your attention to the Delta versus IV graph and in

particular look at the Call Option delta when implied volatility is high (maroon line).

As we can see the delta does not really collapse to zero (like the blue line – CE delta

when IV is low). This should explain why the premium is not really low. Further add

to this the fact that there is sufficient time value, the OTM option tends to have a

‘respectable’ premium.

Download the Volatility Cone excel.

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Key takeaways from this chapter

1. Volatility smile helps you visualize the fact that the OTM options usually have high

IVs

2. With the help of a ‘Volatility Cone’ you can visualize today’s implied volatility with

respect to past realized volatility

3. Gamma is high for ATM option especially towards the end of expiry

4. Gamma for ITM and OTM options goes to zero when we approach expiry

5. Delta has an effect on lower range of options around ATM when IV is low and its

influence increases when volatility is high.

6. When the volatility is high, the far OTM options do tend to have a non zero delta

value

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Module 5 — Options Theory for Professional Trading

Chapter 21

Greek Calculator

127

21.1 – Background

So far in this module we have discussed all the important Option Greeks and their

applications. It is now time to understand how to calculate these Greeks using the

Black & Scholes (BS) Options pricing calculator. The BS options pricing calculator is

based on the Black and Scholes options pricing model, which was first published by

Fisher Black and Myron Scholes (hence the name Black & Scholes) in 1973, however

Robert C Merton developed the model and brought in a full mathematical

understanding to the pricing formula.

This particular pricing model is highly revered in the financial market, so much so

that both Robert C Merton and Myron Scholes received the 1997 Noble Prize for

Economic Sciences. The B&S options pricing model involves mathematical concepts

such as partial differential equations, normal distribution, stochastic processes etc.

The objective in this module is not to take you through the math in B&S model; in

fact you could look at this video from Khan Academy for the same –

My objective is to take you through the practical application of the Black & Scholes

options pricing formula.

21.2 – Overview of the model

Think of the BS calculator as a black box, which takes in a bunch of inputs and gives

out a bunch of outputs. The inputs required are mostly market data of the options

contract and the outputs are the Option Greeks.

The framework for the pricing model works like this:

1. We input the model with Spot price, Strike price, Interest rate, Implied volatility,

Dividend, and Number of days to expiry

2. The pricing model churns out the required mathematical calculation and gives out a

bunch of outputs

3. The output includes all the Option Greeks and the theoretical price of the call and

put option for the strike selected

The illustration below gives the schema of a typical options calculator:

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On the input side:

Spot price – This is the spot price at which the underlying is trading. Note we can

even replace the spot price with the futures price. We use the futures price when

the option contract is based on futures as its underlying. Usually the commodity

and in some cases the currency options are based on futures. For equity option

contacts always use the spot price.

Interest Rate – This is risk free rate prevailing in the economy. Use the RBI 91 day

Treasury bill rate for this purpose. You can get the rate from the RBI website, RBI

has made it available on their landing page, as highlighted below.

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As of September 2015 the prevailing rate is 7.4769% per annum.

Dividend – This is the dividend per share expected in the stock, provided the stock

goes ex dividend within the expiry period. For example, assume today is

September and you wish to calculate the Option Greeks for the ICICI Bank

option contract. Assume ICICI Bank is going ex dividend on 18

Sept with a dividend

of Rs.4. The expiry for the September series is 24

September 2015, hence the

dividend would be Rs.4. in this case.

Number of days to expiry – This the number of calendar days left to expiry

Volatility – This is where you need to enter the option’s implied volatility. You can

always look at the option chain provided by NSE to extract the implied volatility

data. For example, here is the snap shot of ICICI Bank’s 280 CE, and as we can see,

the IV for this contract is 43.55%.

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Let us use this information to calculate the option Greeks for ICICI 280 CE.

o Spot Price = 272.7

o Interest Rate = 7.4769%

o Dividend = 0

o Number of days to expiry = 1 (today is 23

September, and expiry is on

September)

o Volatility = 43.55%

Once we have this information, we need to feed this into a standard Black & Scholes

Options calculator. We do have this calculator on our website

– https://zerodha.com/tools/black-scholes , you can use the same to calculate the

Greeks.

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Once you enter the relevant data in the calculator and click on ‘calculate’, the

calculator displays the Option Greeks –

On the output side, notice the following –

o The premium of 280 CE and 280 PE is calculated. This is the theoretical option price

as per the B&S options calculator. Ideally this should match with the current option

price in the market

o Below the premium values, all the Options Greeks are listed.

I’m assuming that by now you are fairly familiar with what each of the Greeks

convey, and the application of the same.

One last note on option calculators – the option calculator is mainly used to

calculate the Option Greeks and the theoretical option price. Sometimes small

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difference arises owing to variations in input assumptions. Hence for this reason, it

is good to have room for the inevitable modeling errors. However by and large, the

option calculator is fairly accurate.

21.3 – Put Call Parity

While we are discussing the topic on Option pricing, it perhaps makes sense to

discuss ‘Put Call Parity’ (PCP). PCP is a simple mathematical equation which states –

Put Value + Spot Price = Present value of strike (invested to maturity) + Call

Value.

The equation above holds true assuming –

1. Both the Put and Call are ATM options

2. The options are European

3. They both expire at the same time

4. The options are held till expiry

For people who are not familiar with the concept of Present value, I would suggest

you read through this – http://zerodha.com/varsity/chapter/dcf-primer/ (section

14.3).

Assuming you are familiar with the concept of Present value, we can restate the

above equation as –

P + S = Ke

(-rt)

+ C

Where, Ke

(-rt)

represents the present value of strike, with K being the strike itself. In

mathematical terms, strike K is getting discounted continuously at rate of ‘r’ over

time‘t’

Also, do realize if you hold the present value of the strike and hold the same to

maturity, you will get the value of strike itself, hence the above can be further

restated as –

Put Option + Spot Price = Strike + Call options

So why should the equality hold? To help you understand this better think about

two traders, Trader A and Trader B.

o Trader A holds ATM Put option and 1 share of the underlying stock (left hand side of

PCP equation)

o Trader B holds a Call option and cash amount equivalent to the strike (right hand

side of PCP equation)

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This being the case, as per the PCP the amount of money both traders make

(assuming they hold till expiry) should be the same. Let us put some numbers to

evaluate the equation –

Underlying = Infosys

Strike = 1200

Spot = 1200

Trader A holds = 1200 PE + 1 share of Infy at 1200

Trader B holds = 1200 CE + Cash equivalent to strike i.e 1200

Assume upon expiry Infosys expires at 1100, what do you think happens?

Trader A’s Put option becomes profitable and he makes Rs.100 however he loses

100 on the stock that he holds, hence his net pay off is 100 + 1100 = 1200.

Trader B’s Call option becomes worthless, hence the option’s value goes to 0,

however he has cash equivalent to 1200, hence his account value is 0 + 1200 = 1200.

Let’s take another example, assume Infy hits 1350 upon expiry, lets see what

happens to the accounts of both the trader’s.

Trader A = Put goes to zero, stock goes to 1350/-

Trader B = Call value goes to 150 + 1200 in cash = 1350/-

So clearly, irrespective of where the stock expires, the equations hold true, meaning

both trader A and trader B end up making the same amount of money.

All good, but how would you use the PCP to develop a trading strategy? Well, for

that you will have to wait for the next module which is dedicated to “Option

Strategies” J. Before we start the next module on Option Strategies, we have 2 more

chapters to go in this module.

Key takeaways from this chapter

1. The options calculator is based on the Black & Scholes model

2. The Black & Scholes model is used to estimate the option’s theoretical price along

with the option’s Greek

3. The interest rate in the B&S calculator refers to the risk free rate as available on the

RBI site

4. The implied volatility can be fetched from the option chain from the NSE website

5. The put call parity states that the payoff from a put option plus the spot equals the

payoff from call option plus the strike.

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Module 5 — Options Theory for Professional Trading

Chapter 22

Re-introducing Call & Put Options

115

22.1 – Why now?

I suppose this chapter’s title may confuse you. After rigorously going through the

options concept over the last 21 chapters, why are we now going back to “Call & Put

Options” again? In fact we started the module by discussing the Call & Put options,

so why all over again?

Well, this is because I personally believe that there are two learning levels in options

– before discovering option Greeks and after discovering the option Greeks. Now

that we have spent time learning Option Greeks, perhaps it is time to take a fresh

look at the basics of the call and put options, keeping the option Greeks in

perspective.

Let’s have a quick high-level recap –

1. You buy a Call option when you expect the underlying price to increase (you are out

rightly bullish)

2. You sell a Call option when you expect the underlying price not to increase (you

expect the market to either stay flat or go down but certainly not up)

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3. You buy a Put option when you expect the underlying price to decrease (you are out

rightly bearish)

4. You sell a Put option when you expect the underlying price not to decrease (you

expect the market to stay flat or go up but certainly not down)

Of course the initial few chapters gave us an understanding on the call and put

option basics, but the agenda now is to understand the basics of call and put

options keeping both volatility and time in perspective. So let’s get started.

22.2 – Effect of Volatility

We know that one needs to buy a Call Option when he/she expects the underlying

asset to move higher. Fair enough, for a moment let us assume that Nifty is

expected to go up by a certain percent, given this would you buy a Call option if –

1. The volatility is expected to go down while Nifty is expected to go up?

2. What would you do if the time to expiry is just 2 days away?

3. What would you do if the time to expiry is more than 15 days away?

4. Which strike would you choose to trade in the above two cases – OTM, ATM, or ITM

and why would you choose the same?

These questions clearly demonstrate the fact that buying a call option (or put

option) is not really a straightforward task. There is a certain degree of ground work

required before you buy an option. The ground work mainly revolves around

assessment of volatility, time to expiry, and of course the directional movement of

the market itself.

I will not talk about the assessment of market direction here; this is something you

will have to figure out yourself based on theories such as technical analysis,

quantitative analysis, or any other technique that you deem suitable.

For instance you could use technical analysis to identify that Nifty is likely to move

up by 2-3% over the next few days. Having established this, what would you do?

Would you buy an ATM option or ITM option? Given the fact that Nifty will move up

by 2-3% over the next 2 days, which strike gives you maximum bang for the buck?

This is the angle I would like to discuss in this chapter.

Let’s start by looking at the following graph, if you recollect we discussed this in the

chapter on Vega –

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The graph above depicts how a call option premium behaves with respect to

increase in volatility across different ‘time to expiry’ time frames. For example the

blue line shows how the call option premium behaves when there are 30 days to

expiry, green for 15 days to expiry, and red for 5 days to expiry.

With help of the graph above, we can arrive at a few practical conclusions which we

can incorporate while buying/selling call options

1. Regardless of time to expiry, the premium always increases with increase in

volatility and the premium decreases with decrease in volatility

2. For volatility to work in favor of a long call option one should time buying a call

option when volatility is expected to increase and avoid buying call option when

volatility is expected to decrease

3. For volatility to work in favor of a short call option, one should time selling a call

option when volatility is expected to fall and avoid selling a call option when the

volatility is expected to increase

Here is the graph of the put option premium versus volatility –

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This graph is very similar to the graph of call premium versus volatility – therefore

the same set of conclusions hold true for put options as well.

These conclusions make one thing clear – buy options when you expect volatility to

increase and short options when you expect the volatility to decrease. Now the next

obvious question is – which strike to choose when you decide to buy or sell options?

This is where the assessment of time to expiry comes into play.

22.3 – Effect of Time

Let us just assume that the volatility is expected to increase along with increase in

the underlying prices. Clearly buying a call option makes sense. However the more

important aspect is to identify the right strike to buy. Infact when you wish to buy an

option it is important to analyze how far away we are with respect to market expiry.

Selection of strike depends on the time to expiry.

Do note – understanding the chart below may seem a bit confusing in the

beginning, but it is not. So don’t get disheartened if you don’t get it the first time you

read, just give it another shot 

Before we proceed we need to get a grip on the timelines first. A typical F&O series

has about 30 days before expiry (barring February series). To help you understand

better, I have divided the series into 2 halves – the first half refers to the first 15

days of the series and the 2

half refers to the last 15 days of the F&O series. Please

do keep this in perspective while reading through below.

Have a look at the image below; it contains 4 bar charts representing the

profitability of different strikes. The chart assumes –

1. The stock is at 5000 in the spot market, hence strike 5000 is ATM

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2. The trade is executed at some point in the 1

half of the series i.e between the start

of the F&O series and 15

of the month

3. We expect the stock to move 4% i.e from 5000 to 5200

Given the above, the chart tries to investigate which strike would be the most

profitable given the target of 4% is achieved within –

1. 5 days of trade initiation

2. 15 days of trade initiation

3. 25 days of trade initiation

4. On expiry day

So let us start from the first chart on the left top. This chart shows the profitability

of different call option strikes given that the trade is executed in the first half of the

F&O series. The target is expected to be achieved within 5 days of trade execution.

Here is a classic example – today is 7

Oct, Infosys results are on 12

Oct, and you

are bullish on the results. You want to buy a call option with an intention of squaring

it off 5 days from now, which strike would you choose?

From the chart it is clear – when there is ample time to expiry (remember we are at

some point in the 1

half of the series), and the stock moves in the expected

direction, then all strikes tend to make money. However, the strikes that make

maximum money are (far) OTM options. As we can notice from the chart, maximum

money is made by 5400 and 5500 strike.

Conclusion – When we are in the 1

half of the expiry series, and you expect the

target to be achieved quickly (say over few days) buy OTM options. In fact I would

suggest you buy 2 or 3 strikes away from ATM and not beyond that.

Look at the 2

chart (top right) – here the assumption is that the trade is executed

in the 1

half the series, the stock is expected to move by 4%, but the target is

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expected to be achieved in 15 days. Except for the time frame (target to be

achieved) everything else remains the same. Notice how the profitability changes,

clearly buying far OTM option does not makes sense. In fact you may even lose

money when you buy these OTM options (look at the profitability of 5500 strike).

Conclusion – When we in the 1

half of the expiry series, and you expect the target

to be achieved over 15 days, it makes sense to buy ATM or slightly OTM options. I

would not recommend buying options that are more than 1 strike away from ATM.

One should certainly avoid buying far OTM options.

In the 3

chart (bottom left) the trade is executed in the 1

half the series and

target expectation (4% move) remains the same but the target time frame is

different. Here the target is expected to be achieved 25 days from the time of trade

execution. Clearly as we can see OTM options are not worth buying. In most of the

cases one ends up losing money with OTM options. Instead what makes sense is

buying ITM options.

Also, at this stage I have to mention this – people end up buying OTM options simply

because the premiums are lower. Do not fall for this, the low premium of OTM

options creates an illusion that you won’t lose much, but in reality there is a very

high probability for you to lose all the money, albeit small amounts. This is

especially true in cases where the market moves but not at the right speed. For

example the market may move 4% but if this move is spread across 15 days, then it

does not make sense holding far OTM options. However, far OTM options make

money when the movement in the market is swift – for example a 4% move within 1

or say 2 days. This is when far OTM options moves smartly.

Conclusion – When we are at the start of the expiry series, and you expect the

target to be achieved over 25 days, it makes sense to buy ITM options. One should

certainly avoid buying ATM or OTM options.

The last chart (bottom right) is quite similar to the 3

chart, except that you expect

the target to be achieved on the day of the expiry (over very close to expiry).

The conclusion is simple – under such a scenario all option strikes, except ITM lose

money. Traders should avoid buying ATM or OTM options.

Let us look at another set of charts – the idea here is to figure out which strikes to

choose given that the trade is executed in the 2

half of the series i.e at any point

from 15

of the month till the expiry. Do bear in mind the effect of time decay

accelerates in this period; hence as we are moving closer to expiry the dynamic of

options change.

The 4 charts below help us identify the right strike for different time frames during

which the target is achieved. Of course we do this while keeping theta in

perspective.

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Chart 1 (top left) evaluates the profitability of different strikes wherein the trade is

executed in the 2

half of the series and the target is achieved the same day of

trade initiation. News driven option trade such as buying an option owing to a

corporate announcement is a classic example. Buying an index option based on the

monetary policy decision by RBI is another example. Clearly as we can see from the

chart all strikes tend to make money when the target is achieved the same day,

however the maximum impact would be on (far) OTM options.

Do recall the discussion we had earlier – when market moves swiftly (like 4% in 1

day), the best strikes to trade are always far OTM.

Conclusion – When you expect the target to be achieved the same day (irrespective

of time to expiry) buy far OTM options. I would suggest you buy 2 or 3 strikes away

from ATM options and not beyond that. There is no point buying ITM or ATM

options.

Chart 2 (top right) evaluates the profitability of different strikes wherein the trade

is executed in the 2

half of the series and the target is achieved within 5 days of

trade initiation. Notice how the profitability of far OTM options diminishes. In the

above case (chart 1) the target is expected to be achieved in 1 day therefore buying

(far) OTM options made sense, but here the target is achieved in 5 days, and

because the trade is kept open for 5 days especially during the 2

half of the series,

the impact of theta is higher. Hence it just does not make sense risking with far OTM

options. The safest bet under such a scenario is strikes which are slightly OTM.

Conclusion – When you are in the 2

half of the series, and you expect the target to

be achieved around 5 days from the time of trade execution buy strikes that are

slightly OTM. I would suggest you buy 1 strike away from ATM options and not

beyond that.

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Chart 3 (bottom right) and Chart 4 (bottom left) – both these charts are similar

expect in chart 3 the target is achieved 10 days from the trade initiation and in chart

4, the target is expected to be achieved on the day of the expiry. I suppose the

difference in terms of number of days won’t be much, hence I would treat them to

be quite similar. From both these charts we can reach 1 conclusion – far OTM

options tend to lose money when the target is expected to be achieved close to

expiry. In fact when the target is achieved closer to the expiry, the heavier the far

OTM options bleed. The only strikes that make money are ATM or slightly ITM

option.

While the discussions we have had so far are with respect to buying a call option,

similar observations can be made for PUT options as well. Here are two charts that

help us understand which strikes to buy under various situations –

These charts help us understand which strikes to trade when the trade is initiated in

the first half of the series, and the target is achieved under different time frames.

While these charts help us understand which strikes to trade when is the trade is

executed in the 2

half of the series and the target is achieved under different time

frames.

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If you go through the charts carefully you will realize that the conclusions for the

Call options holds true for the Put options as well. Given this we can generalize the

best practices for buying options –

Position Initiation

Target Expectation

Best strike to trade

1st half of the series

5 days from initiation

Far OTM (2 strikes away from ATM)

1st half of the series

15 days from initiation

ATM or slightly OTM (1 strike away from ATM)

1st half of the series

25 days from initiation

Slightly ITM options

1st half of the series

On expiry day

ITM

2nd half of the series

Same day

Far OTM (2 or 3 strikes away from ATM)

2nd half of the series

5 days from initiation

Slightly OTM (1 strike away from ATM)

2nd half of the series

10 days from initiation

Slightly ITM or ATM

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2nd half of the series

On expiry day

ITM

So the next time you intend to buy a naked Call or Put option, make sure you map

the period (either 1

half or 2

half of the series) and the time frame during which

the target is expected to be achieved. Once you do this, with the help of the table

above you will know which strikes to trade and more importantly you will know

which strikes to avoid buying.

With this, we are now at the verge of completion of this module. In the next chapter

I would like to discuss some of the simple trades that I initiated over the last few

days and also share my trade rationale behind each trade. Hopefully the case

studies that I will present in the next chapter will give you a perspective on the

general thought process behind simple option trades.

Key takeaways from this chapter

1. Volatility plays a crucial role in your decision to buy options

2. In general buy options when you expect the volatility to go higher

3. Sell options when you expect the volatility to decrease

4. Besides volatility the time to expiry and the time frame during which the target is

expected to be achieved also matters

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Module 5 — Options Theory for Professional Trading

Chapter 23

Case studies – wrapping it all up!

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23.1 – Case studies

We are now at the very end of this module and I hope the module has given you a

fair idea on understanding options. I’ve mentioned this earlier in the module, at this

point I feel compelled to reiterate the same – options, unlike futures is not a straight

forward instrument to understand. Options are multi dimensional instruments

primarily because it has many market forces acting on it simultaneously, and this

makes options a very difficult instrument to deal with. From my experience I’ve

realized the only way to understand options is by regularly trading them, based on

options theory logic.

To help you get started I would like to discuss few simple option trades executed

successfully. Now here is the best part, these trades are executed by Zerodha

Varsity readers over the last 2 months. I believe these are trades inspired by reading

through the contents of Zerodha Varsity, or at least this is what I was told.

Either ways I’m happy because each of these trades has a logic backed by a mutli

disciplinary approach. So in that sense it is very gratifying, and it certainly makes a

perfect end to this module on Options Theory.

Do note the traders were kind enough to oblige to my request to discuss their

trades here, however upon their request I will refrain from identifying them.

Here are the 4 trades that I will discuss –

1. CEAT India – Directional trade, inspired by Technical Analysis logic

2. Nifty – Delta neutral, leveraging the effect of Vega

3. Infosys – Delta neutral, leveraging the effect of Vega

4. Infosys – Directional trade, common sense fundamental approach

For each trade I will discuss what I like about it and what could have been better. Do

note, all the snapshots presented here are taken by the traders themselves, I just

specified the format in which I need these snapshots.

So, let’s get started.

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23.2 – CEAT India

The trade was executed by a 27 year old ‘Options newbie’. Apparently this was his

first options trade ever.

Here is his logic for the trade: CEAT Ltd was trading around Rs.1260/- per share.

Clearly the stock has been in a good up trend. However he believed the rally would

not continue as there was some sort of exhaustion in the rally.

My thinking is that he was encouraged to believe so by looking at the last few

candles, clearly the last three day’s trading range was diminishing.

To put thoughts into action, he bought the 1220 (OTM) Put options by paying a

premium of Rs.45.75/- per lot. The trade was executed on 28

September and expiry

for the contract was on October 29th. Here is the snapshot of the same –

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I asked the trader few questions to understand this better –

1. Why did you choose to trade options and not short futures?

1. Shorting futures would be risky, especially in this case as reversals could be sharp

and MTM in case of sharp reversals would be painful

2. When there is so much time to expiry, why did I choose to trade a slightly OTM

option and not really far OTM option?

1. This is because of liquidity. Stock options are not really liquid, hence sticking to

strikes around ATM is a good idea

3. What about stoploss?

1. The plan is to square off the trade if CEAT makes a new high. In other words a new

high on CEAT indicates that the uptrend is still intact, and therefore my contrarian

short call was flawed

4. What about target?

1. Since the stock is in a good up trend, the idea is to book profits as soon as it’s

deemed suitable. Reversals can be sharp, so no point holding on to short trades. In

fact it would not be a bad idea to reverse the trade and buy a call option.

5. What about holding period?

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1. The trade is a play on appreciation in premium value. So I will certainly not look at

holding this to expiry. Given that there is ample time to expiry, a small dip in stock

price will lead to a decent appreciation in premium.

Note – the QnA is reproduced in my own words, the idea here is to produce the gist

and not the exact word to word conversation.

So after he bought CEAT PE, this is what happened the very next day –

Stock price declined to 1244, and the premium appreciated to 52/-. He was right

when he said “since there is ample time to expiry, a small dip in the stock price will

lead to a good increase in option premium”. He was happy with 7/- in profits (per

lot) and hence he decided to close the trade.

Looking back I guess this was probably a good move.

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Anyway, I guess this is not bad for a first time, overnight options trade.

My thoughts on this trade – Firstly I need to appreciate this trader’s clarity of

thought, more so considering this was his first options trade. If I were to set up a

trade on this, I would have done this slightly differently.

1. From the chart perspective the thought process was clear – exhaustion in the rally.

Given this belief I would prefer selling call options instead of buying them. Why

would I do this? – Well, exhaustion does not necessarily translate to correction in

stock prices. More often than not, the stock would enter a side way movement

making it attractive to option sellers

2. I would select strikes based on the normal distribution calculation as explained

earlier in this module (needless to say, one had to keep liquidity in perspective as

well)

3. I would have executed the trade (selling calls) in the 2

half of the series to benefit

from time decay

Personally I do not prefer naked directional trades as they do not give me a visibility

on risk and reward. However the only time when I initiate a naked long call option

(based on technical analysis) trade is when I observe a flag formation –

1. Stock should have rallied (prior trend) at least 5-10%

2. Should have started correcting (3% or so) on low volumes – indicates profit booking

by week hands

I find this a good setup to buy call options.

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23.3 – RBI News play (Nifty Options)

This is a trade in Nifty Index options based on RBI’s monetary policy announcement.

The trade was executed by a Varsity reader from Delhi. I considered this trade

structured and well designed.

Here is the background for this trade.

Reserve Bank of India (RBI) was expected to announce their monetary policy on

September. While it is hard for anyone to guess what kind of decision RBI would

take, the general expectation in the market was that RBI would slash the repo rates

by 25 basis points. For people not familiar with monetary policy and repo rates, I

would suggest you read this –

http://zerodha.com/varsity/chapter/key-events-and-their-impact-on-markets/

RBI’s monetary policy is one of the most eagerly awaited events by the market

participants as it tends to have a major impact on market’s direction.

Here are few empirical market observations this trader has noted in the backdrop

market events –

1. The market does not really move in any particular direction, especially 2 – 3 days

prior to the announcement. He find this applicable to stocks as well – ex : quarterly

results

2. Before the event/announcement market’s volatility invariably shoots up

3. Because the volatility shoots up, the option premiums (for both CE and PE) also

shoot up

While, I cannot vouch for his first observations, the 2

and 3

observation does

make sense.

So in the backdrop of RBI’s policy announcement, ample time value, and increased

volatility (see image below) he decided to write options on 28

of September.

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Nifty was somewhere around 7780, hence the strike 7800 was the ATM option. The

7800 CE was trading at 203 and the 7800 PE was trading at 176, both of which he

wrote and collected a combined premium of Rs.379/-.

Here is the option chain showing the option prices.

I had a discussion with him to understand his plan of action; I’m reproducing the

same (in my own words) for your understanding –

1. Why are you shorting 7800 CE and 7800 PE?

1. Since there was ample time to expiry and increased volatility, I believe that the

options are expensive, and premiums are higher than usual. I expect the volatility to

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decrease eventually and therefore the premiums to decrease as well. This would

give me an opportunity to buyback both the options at a lower price

2. Why did you choose to short ATM option?

1. There is a high probability that I would place market orders at the time of exit, given

this I want to ensure that the loss due to impact cost is minimized. ATM options

have lesser impact cost, therefore it was a natural choice.

3. For how long do you plan to hold the trade?

1. Volatility usually drops as we approach the announcement time. From empirical

observation I believe that the best time to square of these kinds of trade would be

minutes before the announcement. RBI is expected to make the announcement

around 11:00 AM on September29

; hence I plan to square off the trade by 10:50

AM.

4. What kind of profits do you expect for this trade?

1. I expect around 10 – 15 points profits per lot for this trade.

5. What is you stop loss for this trade?

1. Since the trade is a play on volatility, its best to place SL based on Volatility and not

really on the option premiums. Besides this trade comes with a predefined ‘time

based stoploss’ – remember no matter what happens, the idea is to get out minutes

before RBI makes the announcement.

So with these thoughts, he initiated the trade. To be honest, I was more confident

about the success of this trade compared to the previous trade on CEAT. To a large

extent I attribute the success of CEAT trade to luck, but this one seemed like a more

rational set up.

Anyway, as per plan the next day he did manage to close the trade minutes before

RBI could make the policy announcement.

Here is the screenshot of the options chain –

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As expected the volatility dropped and both the options lost some value. The 7800

CE was trading at 191 and the 7800 PE was trading at 178. The combined premium

value was at 369, and he did manage to make a quick 10 point profit per lot on this

trade. Not too bad for an overnight trade I suppose.

Just to give you a perspective – this is what happened immediately after the news hit

the market.

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My thoughts on this trade – In general I do subscribe to the theory of volatility

movement and shorting options before major market events. However such trades

are to be executed couple of days before the event and not 1 day before.

Let me take this opportunity to clear one misconception with respect to the

news/announcement based option trades. Many traders I know usually set up the

opposite trade i.e buy both Call and Put option before major events. This strategy is

also called the “Long Straddle”. The thought process with a long straddle is straight

forward – after the announcement the market is bound to move, based on the

direction of the market movement either Call or Put options will make money. Given

this the idea is simple – hold the option which is making money and square off the

option that is making a loss. While this may seem like a perfectly logical and intuitive

trade, what people usually miss out is the impact of volatility.

When the news hits the market, the market would certainly move. For example if

the news is good, the Call options will definitely move. However more often than

not the speed at which the Put option premium will lose value is faster than

the speed at which the call option premium would gain value. Hence you will

end up losing more money on the Put option and make less money on Call option.

For this reasons I believe selling options before an event to be more meaningful.

23.4 – Infosys Q2 Results

This trade is very similar to the previous RBI trade but better executed. The trade

was executed by another Delhiite.

Infosys was expected to announce their Q2 results on 12

October. The idea was

simple – news drives volatility up, so short options with an expectation that you can

buy it back when the volatility cools off. The trade was well planned and the position

was initiated on 8

Oct – 4 days prior to the event.

Infosys was trading close to Rs.1142/- per share, so he decided to go ahead with the

1140 strike (ATM).

Here is the snapshot at the time of initiating the trade –

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On 8

October around 10:35 AM the 1140 CE was trading at 48/- and the implied

volatility was at 40.26%. The 1140 PE was trading at 47/- and the implied volatility

was at 48%. The combined premium received was 95 per lot.

I repeated the same set of question (asked during the earlier RBI trade) and the

answers received were very similar. For this reason I will skip posting the question

and answer extract here.

Going back to Infosys’s Q2 results, the market’s expectation was that Infosys would

announce fairly decent set of number. In fact the numbers were better than

expected, here are the details –

“For the July-September quarter, Infosys posted a net profit of $519 million,

compared with $511 million in the year-ago period. Revenue jumped 8.7 % to $2.39

billion. On a sequential basis, revenue grew 6%, comfortably eclipsing market

expectations of 4-4.5% growth.

In rupee terms, net profit rose 9.8% to Rs.3398 crore on revenue of Rs. 15,635 crore,

which was up 17.2% from last year”. Source: Economic Times.

The announcement came in around 9:18 AM, 3 minutes after the market opened,

and this trader did manage to close the trade around the same time.

Here is the snapshot –

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The 1140 CE was trading at 55/- and the implied volatility had dropped to 28%. The

1140 PE was trading at 20/- and the implied volatility had dropped to 40%.

Do pay attention to this – the speed at which the call option shot up was lesser than

the speed at which the Put option dropped its value. The combined premium was

75 per lot, and he made a 20 point profit per lot.

My thoughts on this trade – I do believe this trader comes with some experience;

it is quite evident with the trade’s structure. If I were to execute this trade I would

probably do something very similar.

23.5 – Infosys Q2 aftermath (fundamentals based)

This trade was executed by a fellow Bangalorean. I know him personally. He comes

with impressive fundamental analysis skills. He has now started experimenting with

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options with the intention of identifying option trading opportunities backed by his

fundamental analysis skills. It would certainly be interesting to track his story going

forward.

Here is the background to the trade –

Infosys had just announced an extremely good set of numbers but the stock was

down 5% or so on 12

Oct and about 1% on 13

Oct.

Upon further research, he realize that the stock was down because Infosys cut down

their revenue guidance. Slashing down the revenue guidance is a very realistic

assessment of business, and he believed that the market had already factored this.

However the stock going down by 6% was not really the kind of reaction you would

expect even after markets factoring in the news.

He believed that the market participants had clearly over reacted to guidance value,

so much so that the market failed to see through the positive side of the results.

His belief – if you simultaneously present the markets good news and bad news,

market always reacts to bad news first. This was exactly what was going on in

Infosys.

He decided to go long on a call option with an expectation that the market will

eventually wake up and react to the Q2 results.

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He decided to buy Infosys’s 1100 CE at 18.9/- which was slightly OTM. He planned to

hold the trade till the 1100 strike transforms to ITM. He was prepared to risk Rs.8.9/-

on this trade, which meant that if the premium dropped to Rs.10, he would be

getting out of the trade taking a loss.

After executing the trade, the stock did bounce back and he got an opportunity to

close the trade on 21

Oct.

Here is the snapshot –

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He more than doubled his money on this trade. Must have been a sweet trade for

him

Do realize the entire logic for the trade was developed using simple understanding

of financial statements, business fundamentals, and options theory.

My thoughts on this trade – Personally I would not be very uncomfortable

initiating naked trades. Besides in this particular while the entry was backed by

logic, the exit, and stoploss weren’t. Also, since there was ample time to expiry the

trader could have risked with slightly more OTM options.

And with this my friends, we are at the end of this module on Options Theory!

I hope you found this material useful and I really hope this makes a positive impact

on your options trading techniques.

Good luck.

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